Gemara

48a (Beraisa - Rebbi): A Nazir may not be Mitamei "l'Imo (for his mother)." It says the same about a Kohen Gadol, even though a Kal va'Chomer teaches this, so "l'Imo" is free for a Gezeirah Shavah. Just like a Nazir may be Mitamei from relatives' Tzara'as or emissions, but not to their corpses, also a Kohen Gadol.

48b (Beraisa) Suggestion: If one was going to slaughter his Korban Pesach or circumcise his son, and he heard that a relative died, perhaps he should be Mitamei to bury the relative!

Rejection: "He will not become Tamei."

Suggestion: Perhaps he is not Mitamei even for a Mes Mitzvah!

Rejection: He is not Mitamei "l'Achoso (for his sister)", but he is for a Mes Mitzvah.

R. Akiva says, "Mes" forbids Tum'ah for relatives. "L'Aviv" and "l'Imo" he may not be Mitamei, but he may be Mitamei for a Mes Mitzvah. A Nazir Kohen Gadol may not be Mitamei "for his brother", but he may be Mitamei for a Mes Mitzvah. "Ul'Achoso" teaches like above, if one was going to slaughter his Pesach...

Question: How is R. Akiva able to learn Rebbi's Gezeirah Shavah?

Answer: Since "for his brother" permits a Nazir Kohen Gadol to be Mitamei for a Mes Mitzvah, surely the same applies to any Kohen Gadol. "L'Aviv ul'Imo" is free.

49a: The Torah needed to write both "l'Aviv" and "l'Imo" Had it written only "l'Aviv", we would forbid Tum'ah for his father (perhaps it is not his father), but permit for his mother. Had it written only "l'Imo", we would forbid Tum'ah for his mother, but permit for his father, for his lineage comes from him!

48b - Question: How does R. Yishmael expound "ul'Achoso "? (He assumed that a Mes Mitzvah overrides even two Lavim. If so, it overrides also Mitzvos Aseh!)

Answer: One might have thought that a Mes Mitzvah overrides only Lavim, but not Pesach or Milah, for which there is Kares. The verse refutes this.

Sukah 25a (Beraisa): "B'Shivtecha b'Veisecha" exempts (from Kri'as Shma) someone engaged in a Mitzvah. "Uv'Lechtecha va'Derech" exempts a Chasan. This is the source to exempt one who marries a virgin.

Question: There is a different source for this!

(Beraisa - R. Yitzchak): "There were Tamei people (who could not offer Korban Pesach)" - they engaged in a Mes Mitzvah, and their seventh day was Erev Pesach.

Answer: Had the Torah taught only that a Mes Mitzvah overrides Pesach, we would say that this is because the Chiyuv for Pesach did not come yet, but a Chasan is not exempted from Shma after the Chiyuv came. Had the Torah taught only about a Chasan, we would say that this is because there is no Kares for Shma, but nothing overrides Pesach, for which there is Kares for neglecting it.

Zevachim 99b: R. Shimon holds that an Onen may offer only Korban Pesach (through a Shali'ach).

Question (Beraisa - R. Shimon): "Shelamim" - one must be Shalem (settled, i.e. not an Onen) to bring this Korban. The same applies to Bechor, Ma'aser and Pesach, for they are not brought due to sin, like Shelamim.

Answer #1 (Abaye): If the Mes died in the morning of the 14th, (Aninus preceded the Chiyuv to bring Pesach, so) the Onen must become Tamei. If he died after midday, the Onen brings Pesach (the Chiyuv preceded and overrides Aninus).

Support - (Beraisa #1): "Lah Yitama" is a Mitzvah (for a regular Kohen to become Tamei to bury one of his seven close relatives). If he does not want to become Tamei, we force him. A case occurred in which Yosef ha'Kohen's wife died on Erev Pesach. The other Kohanim forced him to become Tamei against his will.

Contradiction (Beraisa #2): "Ul'Achoso" teaches that if one was going to slaughter his Pesach, and a relative died, he does not Metamei himself. Rather, he does his Mitzvah. However, he is Mitamei for a Mes Mitzvah. (Beraisa #1 holds that Tum'as Kerovim overrides Korban Pesach!)

Answer: He is Mitamei for a relative only if he died before midday.

Answer #5 (Rava): The Mes died after Chatzos. If he died before slaughter and Zerikah of the Onen's Pesach, he does not bring Pesach (he is not Shalem). If he died after slaughter and Zerikah, the Onen eats the Pesach at night!

Rishonim

Rambam (Hilchos Korban Pesach 6:9): If one's relative died on Erev Pesach after midday, after the Chiyuv to offer Pesach came, we slaughter Pesach for him and he eats it at night. This is because Aninus Laylah is mid'Rabanan. If the relative died before midday, we do not slaughter Pesach for him. He is postponed to Pesach Sheni. If they slaughtered and did Zerikah for him, he eats it at night.

Rambam (Hilchos Kil'ayim 10:29): Kavod ha'Briyos does not override a Lav of the Torah. A Mes Mitzvah overrides (Tum'as Nazir or Kohen), for it says "ul'Achoso."

Tosfos (Sukah 25b DH Mishum): In Zevachim, we say that one going to slaughter his Pesach is Mitamei (for a relative only before midday, but) for a Mes Mitzvah even after midday. Here (in Sukah), we permit for a Mes Mitzvah only before the Chiyuv came! We must say that here we do not discuss a proper Mes Mitzvah, rather, a relative. He may be Mitamei before midday, like Yosef ha'Kohen. However, this is difficult for Rava, who permits for relatives even after midday.

Note: If even relatives may not be Mitamei after midday, who will bury the Mes? It will be a Mes Mitzvah! Perhaps indeed, it is a Mes Mitzvah, and only those needed for burial are Mitamei, but not all relatives. Alternatively, we seek people who are already Tamei to bury them.

Question: Why did the Rambam omit that a Mes Mitzvah overrides Pesach and Milah? It is not in the Mishnah Torah, Perush ha'Mishnayos or Sefer ha'Mitzvos!

Answer #1 (Tzlach Berachos 20a DH She'ani): Our Sugya is like R. Yishmael and R. Akiva, who hold that we learn from a Gezeirah Shavah that is free on one side, and do not challenge it. The Halachah is, we challenge it. Therefore, "l'Imo" must be free on both sides, and we lack the last Drashah to teach that a Mes Mitzvah overrides Pesach. This is why the Rambam (Hilchos Kil'ayim 10:29) learns from "ul'Achoso" that a Nazir may be Mitamei for a Mes Mitzvah, unlike our Sugya, which learned from '"ul'Achiv". However, the Rambam should rule like Rava (Megilah 3b), who learns from "ul'Achoso" that a Mes Mitzvah overrides Avodah!

Answer #2 (Or Some'ach Korban Pesach 6:9 DH v'Da): The Rambam was unsure about the correct text of Rava. His text said that if the Mes died before midday, and they offered his Pesach, he eats at night, because Aninus Laylah is mid'Rabanan. If so, 'when he is Shalem' is not a proper Drashah. The Torah allows offering his Korban! The Beraisa forbids Tum'ah for his sister when she died before midday, for then he can fulfill Pesach. However, once Chachamim decreed not to offer his Korban, in any case he cannot fulfill Pesach, so he is Mitamei. A Mes Mitzvah is Docheh Pesach only if it was in the morning, before the Chiyuv came. The Rambam was forced to say so due to Yevamos 7a. "Ul'Achoso" teaches that a Mes Mitzvah overrides Avodah, not Pesach, for the Tzibur is obligated to prepare for Korbanos Tzibur even beforehand.