What is the significance of the word "Vayashkimu"?
Rashi: The Satan encouraged them to get up early to sin. 1
Why does the Torah write "le'Echol ve'Shaso" and not "le'Echol ve'Lishtos"?
Oznayim la'Torah (citing the Tanchuma): "Veshaso" implies that they were already drunk. 1 Otherwise, it is inconceivable that people who saw the Kavod of the Shechinah at Har Sinai should should indulge in diolaytry - 'whilst the King was still celebrating!'
Oznayim la'Torah: As the Navi hints in Yeshayah, 28:7.
What are the connotations of "Vayakumu Letzachek"?
Ramban: It meanss thaat the people sat down to eat their fill, to inebriate themselves and to rejoice and celebrate with their newfound 'god'. 4
Targum Yonasan: It refers to Avodah Zarah.
Oznayim la'Torah: Refer to 32:6:2:1; At Har Sinai, when they ate from Hashem's Table, the Torah wrote "Vayechezu es ha'Elokim Vayochlu Vayishtu"; whereas here, when they ate from 'the sacrifices of the dead' it says "Vayakumu Letzachek" - Avodah Zarah, Giluy Arayos and Shefichus Damim!
See Bereishis 39:17 (Rashi).
As in Shmuel 2, 2:14 - and here as well, they murdered Chur (when he tried to stop them).
Which the Torah inserts here to explain the "Kol Anos" that Moshe heard. See 32:18 (Ramban). This actually took place after they prostrated themselves to the calf and worshipped it, in 32:8. See Ramban.
To whom did they offer the Korbanos?
Ramban #1: They offered them to Hakadosh-Baruch-Hu. 1
Ramban #2: Although Aharon brought the Korbanos (on the people's behalf) in the Name of Hashem, they prostrated themselves to the Eigel and had in mind that the Korbanos were in its honor, thereby rendering them Pasul. 2
Ramban #2 and Moshav Zekenim #1: Some offered to the calf, and some offered it to Hashem. Regarding the former, Hashem said (in Pasauk 8) "va'Yishtachavu Lo."
Ramban #3 and Moshav Zekenim #2: Aharon offered the Korbanos to Hashem, and the people (the owners) had the calf in mind. 3 Their intention was Mefagel (disqualified the Korbanos).
Hadar Zekenim: They offered it to Hashem, in honor of the calf, like Yisrael did when they inaugurated Sha'ul.
As per Aharon's intentions - Refer to 32:5:2:2 - Seeing as the Torah does not say "Vaya'alu lo Olos Vayagishu lo Shelamim". Refer also to 32:6:151:2 & 3.
Ramban and Moshav Zekenim: In which case, their intention was Mefagel (disqualified) the Korbanos.
