Were Aharon and his sons obligated to spend the entire seven day period, nights included, at the entrance of the Ohel Mo'ed?
Ramban: The obligation not to leave the entrance for seven days was restricted to the duration of the Avodah (which included the burning of the Chalavim by night) 1 - and it extended to future generations as well.
Seforno: Since the curtains were not dismantled, they were obligated to remain at the entrance of the Ohel Mo'ed for the entire seven days.
Ramban: They were permitted to go home once the Avodah for that day was finished, as the Torah writes in 21:12 "u'min ha'Mikdash Lo Yeitzei, ve'Lo Yechalel" - implying that the Kohen Gadol may leave the Beis-ha'Mikdash as long as he does not desecrate the Avodah. In any event, Moshe dismantled the Mishkan every evening after the completion of the Avodah, as stated by Targum Yonasan.
Why does the Torah need to mention that if Aharon and his sons remain at the entrance of the Ohel Mo'ed, like they are commanded, they will not die? Is it not obvious?
Rashi: In order to extrapolate that if they fail to do so, they will die. 1
And this extends to any Kohen Gadol in the future who leaves the Avodah before its conclusion. See Ramban. .
Why did Aharon and his sons sit at the entrance of the Ohel Mo'ed for seven days?
Yerushalmi Mo'ed Katan, 3:4: To mourn for the imminent death of Nadav and Avihhu ? just like Hashem mourned for the imminent destruction of the world prior to the Flood. 1 And this is the source for Aveilus min ha'Torah. 2
See No'ach, Bereishis, 7:10. See also Oznayim la'Torah, who elaborates at lehgth.
See Torah Temimah, note 17, who explains that this is really an Asmachcta (a Mitzvah de'Rabbanan that is hinted in the Torah)..
What are the ramifications of the phrase "u'Shemartem es Mishmeres Hashem"?
Yoma, 5b: It teaches us that whatever is mentioned in connection with the Milu'im is Me'akev (crucial to the Avodah). 1
See Torah Temimah, note 18
Having written "Ka'asher Tzivah Hashem" in Pasuk 34, why does the Torah add "Ki Chein Tzuveisi"?
Yoma, 5b: To teach us that whatever is mentioned in connection with the Milu'im is crucial.