How did they become Tamei Nefesh?
Moshav Zekenim (like R. Yosi ha'Gelili, Sukah 25a): They were Tamei due to Yosef's coffin. 3
Moshav Zekenim (like R. Akiva, Sukah 25b): They were Misha'el and Elitzafan. They were Tamei due to taking Nadav and Avihu out of the Mishkan.
What exactly, was their request?
Rashi: When Moshe told them that Kodshim cannot be brought b'Tum'ah, they asked why the blood could not be sprinkled b'Taharah, and allow them to eat it b'Taharah 1 (at night, they will be Tehorim).
Seforno: They claimed that, since they hade become Tamei due to a Mitzvah, why should it result in the sin of not bringing the Korban Pesach?
Riva: They said that "b'Mo'ado" permits even b'Tum'ah. They did not distinguish between a Tzibur and an individual.
According to the version of Mizrachi
Why did this episode have to come about for the Parshah of Pesach Sheni to come out? Why did Moshe not simply teach Yisrael about Pesach Sheni directly, like he did the rest of the Torah?
Rashi: The people concerned were Tzadikim, and, based on the principle 'One brings about merits via meritorious people, they merited to be responsible for the introduction of Pesach Sheni to Klal Yisrael.
Why did the questioners add the word "b'Mo'ado"?
Seforno: They were asking to be permitted to eat the Pesach b'Tum'ah, since it was a passing Mitzvah whose time would expire the next day.
Rashi writes that due to their merit, Pesach Sheni was taught through them. What was their merit, that they were Tamei?
Moshav Zekenim (8): They engaged in a Mes Mitzvah, and their seventh day was on Erev Pesach. 1
I.e. they were not negligent for not becoming Tahor earlier. Alternatively, they engaged in a Mes Mitzvah, even though their seventh day would be on Erev Pesach, and due to this they might forfeit being able to fulfill Pesach. (PF)