The First 'Zevach'
With this background, we return to our third question (c): why does Yaakov offer specifically "zevachim?"
Significantly, this is the first explicit mention in Chumash of a "zevach"-offering to God. As Ramban (on 46:1) points out, until this time, the children of Noach (and Avraham as well) only offered "olot."
[The technical difference between an "olah" and "zevach" is quite simple. In Sefer Vayikra we learn that an "olah" is entirely consumed by the flame of the mizbayach (chapter 1). In contrast, the meat of a "zevach" - alternately referred to as a "shlamim" (see Vayikra 3:1, 7:11) - is eaten by the owner, while only a small portion is offered on the mizbayach. Conceptually, its name "shlamim" implies a certain "shlaymut" - fullness or completeness, that this voluntary offering can express a feeling of 'completeness' in one's relationship with God. Although it is unclear if at this time Yaakov actually ate these "zevachim," it is significant that the Torah refers to them with the term, "zevach."]
There are three other seminal events in Chumash where specifically "zevachim" are offered:
2) At Ma'amad Har Sinai, Bnei Yisrael offer special "zevachim" as part of the ceremony where they accept the mitzvot:
"Moshe wrote down God's commandments, and then, early in the morning, he set up a mizbayach ... and they offered zevachim, shlamim to God..." (Shmot 24:4-5)Here we find the completion and fulfillment of the ultimate purpose of Yetziat Mitzrayim - Bnei Yisrael's readiness to accept God's commandments.
3) On Yom ha'Shmini, upon the completion of the dedication ceremony of the Mishkan, Bnei Yisrael offer a special korban "shlamim":
"And behold on the 8th day, Moshe called Aharon [to offer special korbanot] ... and an ox and a ram for a shlamim - lizboach - to offer..." (see Vayikra 9:1-4)
One could suggest that Yaakov's offering of "zevachim" points us in very different direction. However anxious (and fearful) Yaakov might be prior to his journey to Egypt, he is also very thankful that Yosef is indeed alive and that he has the opportunity to visit him. These "zevachim" may very well be a "korban todah," a thanksgiving offering! [Note that the "korban todah" is also a category of "shelamim" (see Vayikra 7:11-12).]
Before he departs upon his journey to Egypt, Yaakov thanks God for re-uniting his family. He therefore offers zevachim in Beer Sheva, the site of the mizbayach upon which his father Yitzchak had offered korbanot (see 26:25 and Rashbam 46:1).
Furthermore, considering that the purpose of Yaakov's descent to Egypt is not only to visit Yosef, but also to re-unite his twelve sons, this journey could also be considered the completion of the "bechira" process. Without Yosef, the "bechira" process was not complete, for a very important "shevet" (tribe) was missing. Now, by offering "zevachim," Yaakov thanks God for re-uniting the family and completing the "bechira" process.
We could even take this idea one step further and suggest that while Yaakov asks for Divine permission to leave Eretz Canaan, he offers "zevachim" to explain why he is leaving - in order to unite the twelve tribes and thereby complete the "bechira" process.
This answer to our third question answers our fourth question (d), as well: why does the Torah use Yaakov's special name of Yisrael?
As we explained in our shiur on Parshat Vayishlach, the name Yisrael reflects God's choice of Yaakov as the final stage of the "bechira" process. (See Board #2.) In other words, as opposed to previous generations where only one son was chosen, all of Yaakov's children have been chosen to become God's special nation. Now, as Yaakov descends to Egypt to re-unite his twelve sons, it is only appropriate that the Torah use the name Yisrael.