Bearing in mind that a Chatas generally precedes an Olah (See 5:8), why does the Pasuk give precedence here to the Olah?
Rashi (from Zevachim 90a): The precedence is only l'Mikra'ah, but not for bringing. 1
Why does the Yoledes require atonement?
Ramban, Moshav Zekenim: It is to be purified from the filth that accumulates in the womb when she gives birth. After she has become cleansed, or after the time needed to form the baby, 1 she brings a Korban and becomes Tehorah, since 'Hashem heals all flesh and does wonders'.
Ramban, Moshav Zekenim (citing Nidah, 31b): Because when women suffer labor pains, they tend to swear that they will never again be intimate with their husbands. 2
Da'as Zekenim: Here, and regarding a Metzora 3 , a house with Tzara'as, and a Zav, v'Chiper is not atonemen for sin. It is an expression of cleansing,
A vain Shevu'ah, seeing as she is obligated to her husband in this regard (See Ramban).
Da'as Zekenim: Even though Tzara'as comes to due to Aveiros, the Tzara'as atoned for him. Even though Chachamim expounded that a Yoledes swears not to be intimate with her husband, the verses connote that her Korban is not for sin.
Why does it say "v'Im Lo Yimtza Yadah"?
Moshav Zekenim: We do not tell her to borrow or engage in a trade in order to bring Korban Ashir.
QUESTIONS ON RASHI
Rashi writes that the Olah is first only l'Mikra'ah. What does this mean?
R. Chaim Paltiel, Riva #1, Moshav Zekenim #1: She is Makdish the Olah before the Chatas. 1 A support is "v'Lakchah Shtei Torim
Bartenura: This is because here, Olas ha'Of is in place of Olas Behemah. Elsewhere, both birds are in place of Chatas Behemah, so Chatas ha'Of is Hukdash first. Gur Aryeh - this is wrong. Also regarding Hekdesh, it says (Zevachim 89a) that Chatas is first! Also, it does not say li'Kri'asah, rather, l'Mikra'ah (its verse)! (Riva
Rashi writes that the Chatas is offered first. A Mishnah in Kinim (2:5) says that if a woman brought her Olah and died, her heirs do not bring her Chatas!
Moshav Zekenim: It discusses a Metzora'as. 1 Pesachim 59b says that her Olah comes first.
Moshav Zekenim citing R. Chaim: The case is, she did improperly; b'Di'eved, the Olah is Kosher.
Moshav Zekenim, citing Shmuel Tzarfasi: This cannot be. Toras Kohanim says that it discusses a Yoledes! (I did not find such a Sifra, but also the Rosh (Kinim, Sof Perek 2) cites it. - PF)