Why did they bring specifically a bull as an Olah to purify the Levi'im?
Rashi: Because it is the Korban Tzibur that is designated as an Olah 1 to atone for Avodah-Zarah.
In addition to a goat as a Chatas (15:24).
Having brought a bull as an Olah, why did they bring a second bull as a Chatas, and not a goat - which is the Korban Tzibur for Avodah Zarah?
Rashi: It was a Hora'as Sha'ah (a once-off ruling confined to that occasion).
Why does the Torah add the (otherwise superfluous) word "u?Par Sheini ? Tikach le?Chatas"?
Rashi: To teach us that, like the Olah, it was not to be eaten. 1
Zevachim, 89a: To teach us that the blood of the Chatas is sprinkled after that of the Olah ? whereas ?Va?asei es ha?Echad Chatas ve?es ha?Echad Olah ? in Pasuk 12 ? teaches us that the Chatas is Shechted before the Olah. 2
In spite of the fact that it was a Chatas Chitzonah (whose blood is sprinkled on the Mizbe'ach ha'Olah). See Torah Temimah, note 6.
Zevachim, Ibid.: The limbs of the Olah are burned before the Emurei Chatas, since all the limbs of an Olah are burned - and we learn from here that something that is more holy takes precedence over something that is less holy.
Why was the Chatas not eaten?
Rashi: It was also a Hora'as Sha'ah. 1
Oznayim la'Torah (citing the Sifra): Both the Chatas and the Olah were inaugural sacrifices - like the goat and the calf which were brouight on the eighth day of the Milu'im - in Shemini, Vayikra, 9:3, both of which were burnt. 2
Why does the Torah switch from "Va'lakchu" by the first bull "Tikach" by the second?
Oznayim la'Torah (in Pasuk 12): Although Moshe was commanded to appoint somebody else (Aharon) to bring the two Korbanos, the Torah switches to "Tikach" to hint to him that he too was a Levi, and that he was included in the Kaparah of the two Korbanos. 1
See Oznayim la'Torah (Ibid).
Why does the Torah mention the Olah first regarding taking them, and the Chatas first with regard to the Hakravah (in Pasuk 12)?
Hadar Zekenim: Because, whereas, on the one hand, the better animal should be the Olah, since it is totally burned on the Mizbe'ach, on the other, a Chatas is always offered before an Olah.
Zevachim, 89b: Refer to 8:8:2:2 with regard to the current Pasuk. Regarging Pasuk 12, it teaches us that, since the blood of the Chatas atones, it is sprinkled before that of the Olah..
QUESTIONS ON RASHI
Rashi writes that they should have brought a goat for the Chatas, only it was a Hora'as Sha'ah. The goat is brought for Shogeg, and those who sinned by the Eigel were Meizid, since Moshe tested them like Sotos?
Riva: Really, they should not have brought any Korban at all, since they were Meizid. However, now that they did bring a Korban, it should at least have been the Korban for Shogeg. 1
Riva citing R. Tam: Some people did not believe totally in the Eigel, but they thought that it has some [power]. 2 They were Shogeg, and it was correct to bring a goat to atone for them.
Rashi writes that the Chatas was not eaten (but was burned). How will we reconcile this with what he wrote in Shemini Vayikra, ,9:11 - that the only Chata'os Chitzoniyos that were burned were those of Aharon and the Milu'im?
Riva (Sh'mos 29:14): Also of the Levi'im was Milu'im (to inaugurate them), Rashi means 'except for of Aharon, the Milu'im, and similar matters.'
Moshav Zekenim (Sh'mos 29:14): We can say that the second bull of the Levi'im was an inner Chatas, since they brought it on behalf of the Tzibur.
Moshav Zekenim: There, Rashi discusses Chata'os that were burned on the Mizbe'ach. Here it was not burned on the Mizbe'ach.
