For which sin does the goat of the Chatas come to atone?
Rashi (citing Shevu'os 9a): All the Chata'os of the Musafim come to atone for Tum'as Mikdash ve'Kodashav - if someone ate Kodshim or entered the Mishkan or the Beis ha'Mikdash be'Tum'ah..
Why does the Torah add the word "la'Hashem"?
Rashi #1: The Chatas of Rosh Chodesh 1 atones for sins of Tum'ah in which he was not aware of the Tum'ah, neither at the beginning nor at the end, and only Hashem was aware of it. 2
Rashi #2 (citing a Midrash 3 ) and Targum Yonasan: Hakadosh-Baruch-Hu said 'Bring a Kaparah on My behalf because I reduced the size of the moon!'
Hadar Zekenim: Because it is the first Chatas [taught in Musafim], it says "la'Hashem" to teach that it must be le'Shem Shamayim - and this extends to all of the other Musasim.
Rashi: And we learn other Chata'os of Musafim from the Musaf of Rosh Chodesh. See Sifsei Chachamim.
See Torah Temimah, note 45 and 47.
Sifsei Chachamim: First Rashi cited a Halachic Midrash, and then a Midrash Agadah. Michtav me'Eliyahu (5, p.466) - Change of spiritual influence makes our Avodah harder. It is hard to make our hearts illuminate constantly. Sometimes one questions Hashem's Midos. To fix the lack, Hashem said to bring a Korban. It is worth all the Hester (hiddenness), for the Chidush of seeing the moon appear amidst darkness. Also refer to 28:15:151:1.
Since when does one bring Nesachim together with a Chatas?
Rashi: "ve''Nisko" refers exclusively, to "Olas ha'Tamid" and not to "Se'ir Izim Echad le'Chatas".
QUESTIONS ON RASHI
Rashi writes that Hashem said 'Bring a Kaparah for Me for diminishing the moon!' What are the ramifications of this statement?
Da'as Zekenim (on Pasuk 9): a. It is a consolation for the moon for having been diminished, and b. It prevents children from bring stricken with croup - which is prone to occur on Wednesday, the day of the [new] moon when the luminaries were first put in place. 1
Refer to Bereishis 1:14:151:1.
