Why is the Korban Shelamim called by that name?
Rashi #1: Because it brings Shalom (peace) to the world.
Rashi #2 and Rashbam #1: Because they are shared among the Mizbe'ach, the Kohanim and the owner. 1
Rashbam #2: It is an expression of Tashlumin (payment or fulfillment), seeing as the owner is obligated to fulfill his Neder.
Da'as Zekenim (7:11): It brings Shalom between Yisrael and their Father in Heaven. Similarly, "Zove'ach Todah Yechabdaneni" (Tehilim 50:23) has two Nun's - [he will honor Me] in this world and the world to come.
The Emurim, the Chazeh ve'Shok (the chest and the right calf) and the remainder of the animal, respectively (Rashbam).
Why is an Olah always a male animal, a Shelamim, a male or a female, a [commoner's] 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 "v'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 b'Mezid, one is Chayav Kares), 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): The person was weak like a female and unable to overpower his Yetzer ha'Ra, therefore his Korban is a female. 6
The Ramban's explanation is according to Kabalah, so I have basically translated it without fully comprehending it, with comments taken partially from Rav Chavel's footnotes. (EC)
To a higher plain higher than the Chatas (to 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 Lav ha'Nitak la'Asei.
With the exception of the Chatas of the Nasi (the king [See Ramban])
Chatas is only for Shogeg. It came due to carelessness! Perhaps his Yetzer overpowered him, and therefore he was not careful. (PF)