Why does the Torah discuss the Shelamim, which are Kodshim Kalim, before the Chatas and Asham, which are Kodshei Kodshim?
Oznayim la'Torah: Not just because, like Olah and Minchah, it is a Korban Nedavah, but because Chatas and Asham atone for sins, and unlike Korb'nos Nedavah, which Hashem loves, He would prefer if the sinner would have sinned and would not be required to bring a Kaparah. ? as the Gemara explains in Chagigah, 7a. 1
See Torah Temimah, who elaborates.
Why is the Korban Shelamim so-called?
Rashi #1: Because it brings Shalom (peace) to the world.
Rashbam #2: It is an expression of Tashlumin (payment or fulfillment), seeing as the owner is obligated to fulfill his Neder.
Da'as Zekenim (in 7:11): Because it brings Shalom between Yisrael and their Father in Heaven. 3
Oznayim la'Torah #1: Because, as opposed to other Korbanos, which are connected with sin, Shelamim which are not, indicate the perfect state of the person who brings them. 4
Oznayim la'Torah #2: Because th4ey bring peace to the body (which benefits from the Basar) and to the Neshamah (which benefits from its Kedushah 5 and from bringing the Korban).
Thereby creating an atmosphere of peace.
The Emurim on the Mizbe'ach, the Chazeh ve'Shok (the chest and the right calf) for the Kohanim and the remainder of the animal for the owner (Rashbam).
Da'as Zekenim, Ibid.: "Zove'ach Todah Yechabdan?ni" (Tehilim 50:23) has two Nun's - intimating that [the owner will honor Me] in this world and the world to come.
See Oznayim la'Torah, DH 'Shelamim' and the previous DH, where he elaborates at great length.
See Oznayim la'Torah DH 'Zevach Sheelamim' who elaborates on the combination.
Why is an Olah always a male animal, a Shelamim, a male or a female, a regular Chatas, a female and an Asham, a male?
Ramban 1 : The Olah, as its name suggests, goes up to Heaven. 2 The Shelamim- from the expression "ve'Chol Cheftzi Yashlim" 3 (Yeshayah, 44:28) and "Avanim Sheleimos" 4 (Devarim 27:6). The Chatas, which (is obligatory, and which) comes to atone for a sin (for which be'Meizid, one is Chayav Kareis), is a female animal, 5 whereas ... The Asham (which atones for lesser sins), creates a 'pleasant smell' (like the Olah) and is therefore a male.
Moshav Zekenim (4:28, citing R. Eliezer of Garmaiza): A Chatas is always a female because the owner was weak like a woman and unable to overpower his Yeitzer ha'Ra, therefore his Korban is a female. 6
The Ramban's explanation is according to Kabalah, so I have basically translated it without really understanding it, with comments taken partially from Rav Chavel's footnotes (E.C).
To a higher plain higher than the Chatas (one which is above the Midos).
Because the Shelamim comes to make peace in the world, to come to terms with the Midas ha'Din (which is feminine).
Since it is a total Nedavah - as opposed to the Olah, which is albeit a Nedavah, but which atones for immoral thoughts and for a La'av ha'Nitak la'Asei.
With the exception of the Chatas of the Nasi - the king (See Ramban)
Chatas is only brought for a Shogeg. It came due to carelessness! Perhaps his Yetzer overpowered him, and therefore he was not careful. (PF)
Why does the Torah add the (otherwise superfluous) word "Zevach Shelamim"?
Zevachim, 4a: To teach us that the Shelamim must be Shechted for the sake of a Shelamim (and not S'tam). 1
See Torah Temimah, note 1.
What are the connotations of "Zevach Shelamim Korbano"?
Zevachim, 99b: It implies that someone who is not Shalem 1 (an Onein) may not bring a Korban.
See Torah Temimah, note 3.
In the phrase "Im min ha'Bakar Hu Makriv, what is "Bakar" coming to include and what is "Min" coming to preclude?
Why does the Torah add the (otherwise superfluous) words "Im min ha?Bakar Hu Makriv"?
Sifra: To teach us that only a Yachid can bring a Shalmei Nedavah, but not a Tzibur. 1
See Torah Temimah, note 5, who elaborates.
Seeing as ?min ha?Bakar hu Makriv? implies either a male or a female animal, why does the Torah need to insert "Im Zachar Im Nekeivah"?