To whom is "Lo Seitz'u" referring?
Ramban #1: It refers to Aharon, who was permitted to perform the Avodah 1 in his capacity as Kohen Gadol, and to his sons in the future, but not to the present (since they were On'nim, and not permitted to serve on that day).
Ramban #2: It refers to Aharon's sons in the present as well, who, like their father, were forbidden to leave the area of Pesach Ohel Mo'ed even on that day 2 in honor of the Simchah. 3
Moshav Zekenim (citing Sanhedrin 18a, Sifra, and Mechilta de'Milu'im 28): It refers to Aharon - in his capacity as Kohen Gadol - to teach us that if a Kohen Gadol's relative dies, he is not permitted follow close behind the bier. When the procession moves to a new area, he enters the area that they just vacated. 4
Why does the Torah add "Ki Shemen Mishchas Hashem aleichem"?
Yerushalmi Mo'ed Katan, 3:5: To teach us that seven days Aveilus is d'Oraysa 1 - 'Just as they benifited from the Shemen ha'Mishchah for seven days, so too, shall they 'remain on guard' for their brothers for seven days.
Sifra: To extend the prohibition of leaving the Mishkan during the Avodah to Kohanim of all times.
See Torah Temimah, note 12.
Since Aharon and his sons were forbidden to leave the entrance of the Ohel Mo'ed, how was Elazar able to burn the Parah Adumah on the second of Nisan - for which he would need to go outside the camp - Bamidbar 19:3?
Moshav Zekenim: A Mitzvah is different (this was permitted).
The Sifra learns from the Pasuk in Emor in connection with the Kohen Gadol "u'min ha'Mikdash Lo Yeitzei ve'Lo Yechalel ... " that a Kohen is only forbidden to leave the Mikdash if he desecrates the Avodah, but not whilst the Avodah is not in progress. Consequently, Aharon was able to burn the Parah outside the time of the Avodah.
They were only forbidden to leave the entrance of the Ohel Mo'ed on that day
Proof of this lies in the fact that, in Pasuk 15, Moshe instructed them to eat the Shelamim
