What are the ramifications of "u'Min ha'Mikdash Lo Yeitzei"?
Rashi #1 and Ramban #1: It teaches us that the Kohen Gadol is not permitted to leave the Avodah in order to follow his parents' coffin. 1
Rashi #2 and Ramban #2: If the Kohen Gadol is serving in the Beis-Hamikdash, he does not need to follow his parents' coffin, but may continue to perform the Avodah, even though he is an Onein. 2
What does the Torah mean when it writes "ve'Lo Yechalel Es Mikdash Elokav"?
Rashi 1 and Ramban #1: It means that by not abandoning the Avodah to accompany the dead relative, the Kohen Gadol does not 2 desecrate the Avodah. 3
Ramban #2 and Moshav Zekenim (both citing the B'hag) and Seforno: If he abandons the Avodah in order to bury his deceased parents, he will desecrate the Mikdash of Hashem, 4 by demonstrating that he honors them more than he honors the Mikdash and the Kodesh that are under his jurisdiction.
Rashi: Implying that a Kohen Hedyot who serves whilst he is an Onen, desecrates the Avodah.
Ramban: Neither will he desecrate the Avodah if he does abandon it to bury the relative (See Ramban).
Ramban and Moshav Zekenim: How much more so will he desecrate the Avodah if he abandons it for no good reason (See Ramban, DH 've'Od Matzinu', who elaborates).
What are the implications of "Lo Yeitzei ... ve'Lo Yechalel"?
Zevachim, 15a: It implies that if a Kohen Hedyot Onein does not leave the Beis-Hamikdash - and receives the blood of a Korban, the Korban is Pasul. 1
See Torah Temimah, note 72.
What is the word "Ki Shemen Mishchas Alokav Alav" coming to preclude?
Horayos, 12b: It confines the Heter of an Onein performinh the Avodah to a Kohen Gadol - "Alav", 've'Lo al Chavero' - to precludes a Mashi'ach Milchamah. 1
See Torah Temimah, note 74.
Why does the Torah add the words "Ani Hashem"?
Yerushalmi Sanhedrin, 2:1: To teach us that a Kohen Gadol who sinned and who received Malkos, retains his status of Kohen Gadol - just as Hashem never loses His status. 1
See Torah Temimah, note 75.
QUESTIONS ON RASHI
Rashi writes that the Kohen Gadol does not follow the bier. How distant must he remain, and what is the reason for this?
Ramban#1 (according to R. Meir, Sanhedrin 18a): After the procession enters a new location, he enters the location they just left - and this suffices to remind him not to become Tamei.
Ramban #2 (according to R. Yehudah, Sanhedrin 18a): He does not follow the bier at all, in case, in his grief, he touches and become Tamei. 1
Moshav Zekenim (2, citing R. Simchah): Likewise, relatives for whom a Kohen Hedyot may not become Tamei (maternal siblings, a sister who had Nisu'in), he does not follow the bier, in case in his grief he touches. This is unlike Moshav Zekenim wrote here, that we are not concerned that a Kohen Hedyot might become Tamei for other relatives [if he follows the bier], since he is not so griefstricken about them.