What are the implications of "Shor ... Ki Yivaled"?
Rashi: It implies that only an animal that is born naturally can be brought as a Korban, but not one that is born by caesarian section.
See K'li Yakar.
Why does the Pasuk see fit to specify the three animals individually?
Targum Yonasan: Because the bull represents Avraham
A baby born from two different species.
A sheep that gives birth to a kid-goat, or a goat that gives birth to a lamb.
See Targum Yonasan for additionsl details.
Targum Yonasan: Because nowadays, when there are no Korbanos, we should remember that our Tefilos, which come in place of the Korbanos, are answered on the merit of the Avos (See Na'ar Yonasan).
Why does the Torah insert the words "Ki Yivaled"?
Rashi (in Tehilim, 69:32): To teach us that a calf falls under the category of 'Shor' rom the day it is born.
Why is the reason for the prohibition to slaughter a Korban before the eighth day?
Ba'al ha'Turim: Because on the first day it conveys the impression that one is slaughtering to the heaven and earth, on the second day, to the sky, on the third day, to the sea and dry land, on the fourth, to the celestial luminaries, on the fifth day, to the rodents, on the sixth day, to man. One should therefore wait a full seven days, when it will be clear that he is slaughtering to the G-d who created the world in six days and rested on the seventh.
Targum Yonasan: To ensure that it is not a Nefel (a stillborn baby).
What is the connection between this Parshah and the previous one?
Seforno: Having discussed the blemishes that disqualify an animal from the Mizbe'ach - even though sometimes a blemished animal is worth more than its complete counterpart, and even though one would not hesitate to bring it before one's king 1 - the Torah now discusses perfection in time, forbidding the bringing of animals before the eighth day as Korbanos, slaughtering a mother and her baby on the same day and disqualifying a Korban even with the thought of eating it after its allotted time.
Seforno: Because Hashem, who is perfect, demands physical perfection regarding the animals that are brought before Him and as close to spiritual perfection as is possible regarding those bringing the Korban.
Why is an ox listed first among the Korbanos?
Hadar Zekenim: A parable for this is an esteemed woman who was defamed [about immorality]. The king investigated and found no immorality. He made a feast and seated her at the head, in front of himself, to publicize that the slander was false. The nations deride Yisrael for Chet ha'Egel. Hashem checked, that only the Erev Rav made it - "Shiches Amcha" (refer to Shemos 32:7:4:1), and not My nation - therefore he made the ox the head of the Korbanos.
Why does the Torah forbid offering an animal for a Korban before day eight?
Moshav Zekenim, citing the Rosh: If he offers it during the first six days, it looks like he offers to what was created that day, i.e. Shamayim and Aretz, the firmament, the dry land, the luminaries, Sheratzim, or man. Rather, wait seven days, and know that I created My world in six days and rested on the seventh, and offer it for Me.
Moshav Zekenim, citing R. Eliezer of Garmaiza: The ox that Adam ha'Rishon offered was on day eight from the Creation, for he sinned on Erev Shabbos, and he was not allowed to transgress the first Shabbos [to offer it]. Hashem said, just like he brought on day eight 1 , so [all Korbanos] will be accepted from day eight and onwards.
QUESTIONS ON RASHI
Rashi writes that Ki Yivaled excludes an animal born via Caesarian section. Why do we need another such verse regarding Bechor?
Moshav Zekenim citing the Ri: If not that regarding Bechor, the Torah said that it depends on the first to leave the womb, I would not know to expound here to exclude Yotzei Dofen. And had it written so only about Bechor, I would not learn to other Korbanos, for there are many stringencies special to Bechor.