Duryodhana vs Bhima a analysis.

I don't believe Bhima cheated.
1) Yes Gandhari did not ever open her eyes to look at Duryodhana's body but Duryodhana's body was still made of vajra (lightning/thunderbolt/adamantine/indestructible material).
Narrative:

In days of old. O king, we have obtained thee, by ascetic austerities from Maheswara. The upper part of thy body is wholly made of an assemblage of Vajras, and is, therefore, invulnerable to weapons of every description, O sinless one. The lower part of thy body, capable of captivating the female heart by its comeliness was made of flowers by the goddess herself--the wife of Mahadeva. Thy body is thus, O best of kings, the creation of Maheswara himself and his goddess. Therefore, O tiger among kings, thou art of celestial origin, not human.

Source: http://www.sacred-texts.com/hin/m03/m03250.htm
Bori's version

Analysis: The critical edition also includes this. So it must be true.
Source: Vana Parva Section 240
2) Did Hanuman ever support Bhima in his battles?
Yes but all he did was utter roars, these roars would rob enemies of their lives. But we do not know (who) these enemies were.
KMG
Quote:

Even by thy prowess shall we conquer all foes." Thus addressed, Hanuman said unto Bhimasena, 'From fraternal feeling and affection, I will do good unto thee, by diving into the army of thy foes copiously furnished with arrows and javelins. And, O highly powerful one, O hero, when thou shall give leonine roars, then shall I with my own, add force to shouts. Remaining on the flagstaff of Arjuna's car will I emit fierce shouts that will damp the energy of thy foes. Thereby ye will slay them easily.'

Analysis: Have we ever read any time in the Kurukshetra war that any of Bhima's enemies died due to a roar of Hanuman? No. So we can say that Hanuman was not telling the truth. This is different from BORI CE, because BORI says that the roars will kill people, in kmg it is said that Hanuman's roar will damp the energy of Bhima's enemies. Then Bhima can slay them with ease. But even that is not true as in the main wars none of these roars of Hanuman ever happened.
Source: http://www.sacred-texts.com/hin/m03/m03150.htm
BORI CE

Vana Parva Section 150
Hanuman said that his roars would rob the enemies of their lives.
Look at Duryodhana's death (according to BORI CE).

This has no mention of the roar of Hanuman. It's safe to conclude that Hanuman was exaggerating or that KMG is more correct because it says that Hanuman's roars would help bhima slay them easier. So to see whether Kmg is right or not we will gave to see whether hanuman roared to weaken Duryodhana, but knowing the reality hanuman never ever roared even once during the final fight of Duryodhana. So hanuman supporting Bhima in battles is not true. Only the roars of Duryodhana are mentioned in the death battle.
3) Here is the full text of the mace fight from BORI Critical Edition
(Shalya Parva Section 55):

"The great-souled Pandava raised his club and rushed at the great-souled one. Vrikodara forcefully attacked Dhritarashtra’s son. The elephants present there trumpeted and the horses neighed. The Pandavas desired victory and their weapons blazed."

(Shalya Parva Section 56):
Part 1

"On seeing that Bhimasena had approached, Duryodhana was not distressed in his soul. He roared loudly and attacked him with force. Like horned bulls, they clashed against each other. As they struck each other, there were great and thunderous sounds. That tumultuous battle commenced and it made the body hair stand up. Wishing to triumph, they fought each other in that battle, like Indra and Prahlada.22 The spirited ones fought with clubs and blood covered all their limbs. The greatsouled ones looked like flowering kimshukas. That great and extremely terrible battle raged on. As they roamed around, the sky was beautiful, as if covered with swarms of fireflies.23 That fierce and tumultuous clash raged on for some time. As they fought, both scorchers of enemies were exhausted. Having rested for a short while, those scorchers of enemies again grasped their sparkling clubs and attacked each other. Those immensely valorous bulls among men looked like strong elephants, intolerant with pride and wishing to indulge in intercourse. With clubs in their hands, those infinitely valorous ones glanced towards each other. The gods, the gandharvas and the danavas were overcome by supreme wonder. On seeing Duryodhana and Vrikodara wield those clubs, all the beings were uncertain about who would be victorious. The brothers, supreme among strong ones, attacked each other again."

Part 2

"They circled around each other, seeking to detect a weakness in each other. O king! The spectators saw that they raised those heavy and terrible clubs, which were like Yama’s staff or Indra’s vajra. In that encounter, when Bhimasena struck with his club, in an instant, it produced a terrible and fierce sound. Dhritarashtra’s son saw that Pandava was striking dexterously and powerfully with his club and was astounded. O descendant of the Bharata lineage! As the brave Vrikodara roamed around, executing many different kinds of motions, he looked resplendent. They protected themselves and attacked each other. They repeatedly wounded each other, like hungry cats over food. Bhimasena moved around in many different kinds of motions. He executed circular motions in different spots, wonderful zigzag movements, advancing and retreating. He countered strikes, struck, avoided and chased. He adopted positions that were meant for attack. He defended, restrained himself, leapt up and leapt down. Both of them were skilled in fighting with clubs and wielded them, high and low. The best among the Kuru lineage roamed around in this way, striking each other and avoiding each other. The extremely strong ones sported, executing circular motions. With clubs in their hands, those powerful ones whirled around. O king! Dhritarashtra’s son struck from the right side. Bhimasena struck from the left side. O great king! As Bhima strode around in that field of battle, Duryodhana struck him on his flank. O descendant of the Bharata lineage! When Bhima was thus struck by your son, he whirled his heavy club, thinking about how he should strike. O great king! Bhimasena’s upraised and terrible club was seen to be like Indra’s vajra or like Yama’s staff."

Part 3

"On seeing that Bhimasena was whirling his club around, your son, the scorcher of enemies, raised his terrible club and struck him again. O descendant of the Bharata lineage! Your son’s club descended with the violence of a storm. A tumultuous sound was raised and sparks were generated. Suyodhana was energetic and radiant. As he roamed around and executed many kinds of circular motions, he again got the better of Bhima. When Bhima used his gigantic club to strike with great force, smoke and sparks of fire were generated and there was also a loud and terrible sound. On seeing that Bhimasena was whirling his club, the radiant Suyodhana whirled his heavy club, which possessed the essence of stone. The great-souled one’s club had the violence of a storm. Beholding this, all the Pandus and the Somakas were terrified. They were seen in that encounter, as if they were sporting in the field of battle. Those two scorchers of enemies violently struck each other with their clubs. They were like elephants, goring each other with their tusks. O great king! With blood flowing down, they were beautiful. Thus did the battle, terrible in form, rage on. At the end of the day, it was cruel, like that between Vritra and Vasava. On seeing that Bhima was stationed, your immensely strong son executed wonderful and colourful motions and attacked Kounteya. Bhima became angry. With great force, he struck that golddecorated club.24 O great king! Sparks began to fly and there was a clap, as if lightning was mixed with thunder. O great king! Hurled powerfully by Bhimasena, the club descended and made the earth tremble. Kouravya could not tolerate that his club should be countered in the clash. He was like a crazy elephant, angered at the sight of another elephant. O king! Enraged and having made up his mind, from the left, he powerfully struck Kounteya on the head with the club. O great king! Struck in this way by your son, Pandava Bhima did not tremble and it was extraordinary."

"O king! It was wonderful and all the soldiers honoured him. Despite being struck by the club, Bhima did not waver and did not retreat a step. Bhima, terrible in his valour, picked up a flaming club, decorated with gold, which was heavier and hurled this towards Duryodhana.25 However, displaying his dexterity, the immensely strong Duryodhana freed himself from that thrust and it was extremely wonderful. O king! The club hurled by Bhima was baffled and fell down with the loud noise of a storm and made the earth tremble. Repeatedly resorting to the koushika26 technique of jumping up and circling, he27 discerned when Bhimasena would strike down with the club and deceived him. Having thus deceived Bhima, the immensely strong one, supreme among the Kuru lineage, angrily struck him in the chest with the club. Struck by the club in that great encounter, Bhima was stupefied. Having been struck by your son, he did not know what he should do. O king! At that time, the Somakas and the Pandavas were severely distressed and miserable in their minds. Having been struck, he28 became as enraged as an elephant and attacked your son, like an elephant against another elephant."

"The proud Bhima attacked your son with the club. He rushed forward with force, like a lion against a wild elephant. O king! He was skilled in releasing the club. Approaching the king, he used the club to strike in your son’s direction. Duryodhana was struck in the flank by Bhimasena. He was stupefied by this blow and sank down on his knees on the ground. O lord of the earth! At this, the Srinjayas let out a loud roar. O best of the Bharata lineage! On hearing the roar of the Srinjayas, your son, bull among men, became angry. The mighty-armed one raised himself, like an angry serpent that was sighing. He glanced towards Bhimasena and burnt him down with his sight. With the club in his hand, the great-souled one, best among the Bharata lineage, attacked and, in that clash, struck the great-souled Bhimasena on his head. Bhima was terrible in his valour. Though he was struck on his head, he did not waver, like a mountain. O king! Struck by the club in that encounter, blood began to flow from Partha and he was as beautiful as an elephant with a shattered temple."

Part 4

"Dhananjaya’s brave elder brother then picked up a club that was made out of iron and was capable of slaying heroes. It made a sound like that of the vajra. The destroyer of enemies struck powerfully with this. Struck in this way by Bhimasena, your son fell down, with his body trembling. He was like a blossoming shala tree in a large forest, whirled around by the force of a storm. On seeing that your son had fallen down on the ground, the Pandavas roared in delight. Your son recovered his senses and rose, like an elephant from a lake. The king was always intolerant. He skilfully circled around and struck Pandava, who was stationed before him, making him lose control over his limbs and fall down on the ground. In that encounter, on seeing that the infinitely energetic Bhima had fallen down on the ground, Kourava roared like a lion. Though he29 was like the thunder in his energy, the descent of the club shattered his body armour. At this, a loud roar was heard in the firmament, made by the residents of heaven and the apsaras. The immortals showered down many kinds of excellent flowers. On seeing that the supreme among men had fallen down on the ground, great fear entered the hearts of the enemies. Because of the force of Kourava’s blow, the firm armour had been shattered. However, he30 recovered his senses in a short while and wiped away the blood from his face. Resorting to his fortitude and recovering his strength, Vrikodara dilated his eyes and steadied himself."

(Shalya Parva Section 57):
Part 1

"Understanding the sign, Bhima roamed around with his club in the battle. He executed wonderful circular motions and doubled back. He circled to the right and the left and alternated between the two. O king! Pandava roamed around confounding the enemy. In that fashion, your son was also skilled in executing motions with the club. Wishing to kill Bhimasena, he roamed around, executing dexterous and wonderful motions. They whirled terrible clubs that had been smeared with sandalwood paste and unguents. They were like two angry Yamas, wishing to bring an end to the hostility. Those foremost ones, bulls among men, wished to kill each other. They fought like two Garudas who were after the same serpent. O king! Both of them executed wonderful circular motions."

Part 2

"Because of the descent of the clubs, sparks of fire were generated there. In the encounter, those brave and powerful ones struck each other equally. O king! They were like two oceans agitated by storms. Like crazy elephants, they struck each other equally. Thunderous sounds were generated from the blows of the clubs. That fierce and terrible clash continued. As they fought, both scorchers of enemies were exhausted. Having rested for some time, those scorchers of enemies again angrily grasped their giant clubs and attacked. O Indra among kings! They fought a terrible battle with the descending clubs and severely wounded each other. With eyes like bulls, they spiritedly rushed towards each other. Those brave ones fiercely struck each other, like buffaloes stuck in mud. All their limbs were mangled and they were covered with blood. They looked like two flowering kimshukas on the Himalayas."

Part 3

"Partha showed Duryodhana a weakness and smiling, he suddenly extended himself forwards.34 Vrikodara was learned about fighting. On seeing the advance, the strong one powerfully hurled the club. O lord of the earth! Seeing that the club had been hurled, your son moved from the spot and baffled, it fell down on the ground. Having respectfully warded off that blow, your son, supreme among the Kuru lineage, struck Bhimasena with the club. Struck severely by that blow and with blood flowing down, the infinitely energetic one was stupefied. However, in that encounter, Duryodhana did not realize that Pandava was afflicted. Though his body suffered great pain, Bhima bore himself. He35 thought that he was still steady and ready to strike back in the encounter. That is the reason your son did not strike him again. O king! Having rested for a while, the powerful Bhimasena attacked Duryodhana, who was stationed before him, with force. O bull among the Bharata lineage! On seeing that the angry and infinitely energetic one was attacking, he wished to save himself from the blow."

Part 4

Your great-minded son made up his mind to take a stand. O king! He leapt up, wishing to deceive Vrikodara. However, Bhimasena understood what the king wished to do. He dashed forward, roaring like a lion. O king! As the king leapt up to avoid the blow, Pandava powerfully struck him on the thighs with the club. He was terrible in his deeds and struck with a force like that of the vajra. Duryodhana’s handsome thighs were fractured. The tiger among men fell down, making the earth resound. O lord of the earth! Your son’s thighs were fractured by Bhimasena.

Analysis: In section 56 it is written that Duryodhana decieved Bhima. So rules were already broken by Duryodhana, no one cares if he struck the thighs (it is Duryodhana's job to protect his thighs).
Both Duryodhana and Bhima rested 2 times while the mace fight was continuing to go on and on and on, but Bhima rested a 3rd time.
Bhima was stupified twice. Duryodhana was stupefied twice. Duryodhana got the better of Bhima twice. Ultimately Bhima is the one who won & fought smarter. He took a defensive position but made Duryodhana believe that Bhima was attacking instead of defending. Bhima is the better fighter and defeated Duryodhana, but Duryodhana did perform well, that's all.
Krishna & Arjuna's conversation about this:

Arjuna spoke to the illustrious Vasudeva. ‘Between those two brave ones who are fighting, who do you think is superior? O Janardana! Who possesses the greater qualities? Tell me. Vasudeva replied, ‘They are equal in what they have learnt, but Bhima is stronger. However, Dhritarashtra’s son is superior to Vrikodara because of the efforts that he has undertaken. Using dharma, Bhimasena will not be able to win this encounter. He will be able to kill Suyodhana only if he fights through unfair means. It has been heard that the gods defeated the asuras through the use of maya. The slayer of Bala robbed Vritra of his energy through maya. O Dhananjaya! At the time of gambling with the dice, Bhima took a pledge that in the encounter, he would shatter Suyodhana’s thighs with a club. This destroyer of enemies needs to accomplish that pledge. The king uses maya31 and has to be brought down through maya.

Having made up his mind, he has practised with the club for thirteen years. Wishing to kill Bhimasena, he leaps up and moves diagonally. If the mighty-armed one does not slay him through unfair means, Kourava, Dhritarashtra’s son, will be the king.’ ‘ “Hearing Keshava’s words, the great-souled Dhananjaya glanced in Bhimasena’s direction and slapped his thigh with his hand.33

Analysis: Krishna says that they are equal in knowledge, bhima is superior in strength, Duryodhana ais superior due to his effort. krishna also said that Duryodhana uses deception (maya) to fight, so he can only be defeated by unfair means. Their is nothing wrong in defeating a unfair fighter through unfair methods.
About the roars of hanuman: None of the text states that Hanuman ever roared.
According to Adi parva their was a battle and not just meeting between hanuman and Bhima: "his consequent battle with the mighty Rakshasas and the Yakshas of great prowess including Hanuman;" "Then is narrated the ascent on the hills of Kailasa by Bhimasena, his terrific battle with the mighty Yakshas headed by Hanuman;"
https://www.sacred-texts.com/hin/m01/m01003.htm