Having stated "Kol Peter Rechem," which means the firstborn, why does the Pasuk add "v'Chol Peter Sheger Behemah"?
Rashi #1 and Targum Yonasan: It means 'a firstborn that the mother cast out prematurely' - a Nefel 1 (a stillborn baby), to teach us that a Nefel is considered a Bechor, and it exempts the subsequent baby from the Bechorah.
Rashi #2: Because "Kol Peter Rechem" referred (not to a firstborn animal, but) to a firstborn human baby. 2
Bechoros 3b: To incorpporate a Nefel of Kodshim in the Din of Bechor. 3
Rashi: Even though the term "Sheger" per se is not confined to a Nefel. Refer to Devarim 7:13:2:1, and to Torah Temimah, note 55.
Sifsei Chachamim: In which case "v'Chol Peter Sheger Behemah" does not refer to a Nefel. The question remains however, as to why the Torah then repeats it in the next Pasuk, 13:13?
See Torah Temimah, note 55.
What are the connotations of "v'Ha'avarta"?
Rashi and Ramban: "V'Ha'avarta" is an expression of 'Hafrashah' 1 - separating (or designating). 2
Hadar Zekenim (to 13:11): It means that the Din of Bechor is transferred from that of other sons - to be given to Hashem.
Zevachim 9a: We learn via a Gezerah Shavah "v'Ha'avarta" and "Kol Asher Ya'avor" (Vayikra 27:32 - from Ma'aser Behemah) that, just as, if, after Pesach, one Shechts a leftover Pesach 3 as Ma'aser, it does not take effect, so too, if one Shechts it as a Bechor. 4
Oznayim la'Torah: It is to commemorate Makas Bechoros, in connection with which Hashem said, "v'Avarti b'Eretz Mitzrayim... v'Hikeisi Kol Bechor" (12:12).
Rashi: Like we find in Bamidbar 27:8. See also Torah Temimah, note 54.
Ramban: An animal from the herd; whereas according to Rashi, it refers to Bechor Adam.
Which becomes a Shelamim.
See Torah Temimah, note 53 who elaborates.