What is the significance of the first bull that they brought to purify the Leviyim, as an Olah?
Rashi: The Tzibur brings a bull for an Olah 1 to atone for Avodah-Zarah.
In addition to a goat for a Chatas (15:24).
Why does the Torah add the word "Sheni"?
Rashi: To teach us that, like the Olah, it was not to be eaten. 1
In spite of the fact that it was a Chatas Chitzonah (whose blood was sprinkled on the Mizbe'ach ha'Olah).
Why was the Chatas not eaten?
Rashi: It was a Hora'as Sha'ah (a temporary ruling, confined to that occasion). 1
Rashi: Just as the fact that they brought a bull as the Chatas, and not a goat (See 15:24) was a Hora'as Sha'ah.
Why does it mention the Olah first regarding taking them, and the Chatas first regarding Hakravah (verse 12)?
Hadar Zekenim: The nicer one should be the Olah, for it is totally burned [on the Mizbe'ach]. Chatas is always offered before Olah.
Rashi writes that they should have brought a goat for the Chatas, but it was a Hora'as Sha'ah. The goat is brought for Shogeg. They were Mezid at the Egel, for Moshe tested them like Sotos!
Riva: Really, they should not have brought any Korban, for they were Mezid. Since they brought a Korban, it should have been the Korban for Shogeg. 1
Riva citing R. Tam: Some people did not believe totally in the Egel, but they thought that it has some [power]. 2 They were Shogeg, and it was proper to bring a goat for them.
Rashi writes that the Chatas was not eaten (rather, it was burned). He wrote in Vayikra (9:11) that the only Chata'os Chitzoniyos that were burned were of Aharon and the Milu'im!
Riva (Shemos 29:14): Also of the Leviyim was Milu'im (to inaugurate them), Rashi means 'except for of Aharon, the Milu'im, and similar matters.'
Moshav Zekenim (Shemos 29:14): We can say that the second bull of the Leviyim was an inner Chatas, for they brought it for the Tzibur.
Moshav Zekenim: Here it was not burned on the Mizbe'ach. There, Rashi discusses Chata'os burned on the Mizbe'ach.