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Going by the same rules as OP, No searches
1. How many characters from another great epic Ramayana appeared in Mahabharata? Bonus name them and their significance to this story.
2. Arjuna is known to be the greatest Archer, and developed a skill that no one else mastered as described by Guru Drona himself (even though Karna claimed to have mastered the same skill but was not narrated to have displayed it anywhere). Bonus, contrary to Guru Drona's belief he was shocked to come to know about an incident and an Archer possessing superior Archery skills then Arjuna, who was it and what was the skill?
3. From one of previous posts which had provided some details about the hatred between Krishna and Sisupala, thinking on those lines, there is another important reason behind the enmity between the two due to.... Who was the brother of sisupala, and who slayed him?
4. There are several interesting incidents that happen to the pandavas and in one of those towards the end an animal accompanies the pandavas during their journey to the heaven. Which animal was it and who was in disguise?
5. There were some questions posted earlier related to chariots, but one warriors chariot never touches the ground until a certain point in the story, but eventually does so. When and what event triggered the grounding to happen?

Thanks Dbs Ji for quoting the elaborate number of characters from Ramayana. Of those, Jambavan, the bear who was the minister of the Vanara army in Ramayana also appears again in the Mahabharata and as pointed out in the above reply, was challenged by Krishna to fight with him until death of one of them (believed to be Krishna's trick to prove to this world that Jambavan though was a great warrior but did not get a chance in Ramayan to steal the limelight by killing any famous Rakshas, was equal in strength to Krishna). After his death Krishna marries his daughter.

But I was expecting another most important character too. It's none other than Parasurama who appeared in both Ramayana and Mahabharata, and was believed to have existed even during the previous Yugas. He plays a pretty significant role in this great epic. Amba the princess and eldest daughter of king of Kashi, reaches Parasurama finally for help, after several failed attempts to take revenge on Bhisma Pitama after she vows to kill Bhisma, after he forcibly takes the other two daughters of Kashi and gets them married to Vichitravirya.

Parasurama was Bhisma's guru earlier and taught him Archery and all warfare skills. But he accepts her request and then agrees to fight with Bhisma and vows either make him marry her or never stops fighting with him until he's killed. According to the epic, the war between Bhisma pitama and Parasurama was described as the longest (24 days), non stop, most terrifying and the greatest war in the whole epic, even though no lives were lost, but if it had continued, according the epic, the whole world would have been destroyed wiping out all lives on earth.

"Can anyone identify, who were the other two significant disciples of Guru Parasurama"

I liked your friend's quote of Mainda-dvivida, since they themselves were monkey warriors and were Ashwini kumaras. In Ramayana, Hanuman himself in one instance, specifically quotes that he does not need the help of whole monkey army or anyone to defeat Ravana and his whole army, but just he needs Mainda-dvivida to go along with him to fight them. Such was the greatness of these two warriors. Nakula and Sahadeva were the two Ashwini kumaras in Mahabharata and were gifted with medical powers.

Yama Dharma in the form of Dog, accompanied Yudhi and the pandavas to heaven and there is a story behind the same. Yama Dharma appears thrice before Yudhi in the epic for specific reasons (important one of them is to save him and to test Yudhi's knowledge about the Truth, Shastras and Veda)