1) THE REQUIREMENT FOR A JEW TO GO TO THE MIKVAH AFTER CIRCUMCISION
QUESTION: Beis Shamai and Beis Hillel argue about whether a convert who becomes circumcised on Erev Pesach and immerses in a Mikvah that day is allowed to eat the Korban Pesach that night. The Gemara says that everyone agrees that a Jew who did not have a Milah until Erev Pesach may eat the Korban Pesach that night, after he immerses in a Mikvah.
A convert must immerse as part of his conversion process. Why must a newly circumcised Jew immerse? (TOSFOS)
(a) The TOSFOS YOM TOV answers that every Jew is obligated to make himself Tahor for the Yom Tov (Beitzah 16b). The Tevilah to which the Gemara here refers is completely unrelated to the Bris Milah.
(b) The MINCHAS CHINUCH (#282) answers that a newly circumcised Jew must immerse in a Mikvah because of "Hesech ha'Da'as." Since it is forbidden for an Arel (an uncircumcised man) to eat Kodshim, the Jew, while uncircumcised, presumably was Masi'ach Da'as (removed his attention) and did not guard himself from Tum'ah for the sake of eating Kodshim. He must immerse in a Mikvah because he is Tamei. Similarly, an Onen and a Mechusar Kipurim (91b) must immerse before they eat Kodshim, because they were forbidden to eat Kodshim until now (as Rashi there explains).
(c) The OR ZARU'A writes that a Mumar (apostate) who repented should immerse himself in a Mikvah. Perhaps the Arel mentioned in the Gemara here refers to one who did not circumcise himself out of a spirit of apostasy. He needs to immerse because he was a Mumar who repented.
(d) The SEFAS EMES proposes that both a Jew and a convert alike must wait seven days and have Haza'ah after a Bris Milah. However, this applies to a Jew only as a Gezeirah, because a convert waits seven days and has Haza'ah. The Sefas Emes asserts that this is why Beis Hillel says that "one who separates from his Orlah is considered as though he has separated from the grave"; that is, he is considered Tamei with Tum'as Mes. Only on Erev Pesach did the Rabanan allow him to forgo the seven-day wait and do Haza'ah in order not to miss the Mitzvah of Korban Pesach. However, he is still required to immerse on Erev Pesach as part of the Gezeirah.