What is the meaning of "Atzilei B'nei Yisrael? To whom does it refer?
What does the Torah mean when it writes that "Hashem did not stretch out His Hand"? Why ought He to have done so?
Rashi: He did not stretch out His hand to punish them for gazing at the Shechinah even as they indulged in physical pursuits - whilst they were eating and drinking. 1
Ramban (Pasuk 13, citing Midrash Tanchuma and Rashbam,): He should have stretched out His hand to punish the Zekeinim (except for Yehoshua) for seeing visions of Elokim that they were not worthy of seeing, 2
Seforno: What the Torah means is that, Hashem did not stretch out His Hand to place them in a trance in order that they should prophesy. 3
Hadar Zekenim: Initially they feared being harmed, like it says "Namus Ki Elohim Ra'inu" (Shoftim 13:22; there, they saw only an angel). When they saw that they were not harmed, they received the Shechinah and ate and drank amidst Simchah, and were Chayav Misah.
Da'as Zekenim: He did not stretch out His hand to cover their faces, like he did for Moshe afterwards ("v'Sakosi Kapi Alecha" - 33:22), therefore they saw Elokim. 4
Targum Yonasan: He did not punish Nadav and Avihu, who gazed at the Shechinah, and whose punishment was postponed until the eighth day of the Milu'im, when they died.
Riva: This is haughtiness, like one who prides himself that he may see the king every day. Or, it is feeling informal; they were not awe-stricken from looking, because they felt informal with Him.
Rashbam: This is like (Bamidbar 4:20) "ve'Lo Yavo'u Lir'os ke'Vala es ha'Kodesh, va'Meisu", and like the men of Beis-Shemesh (See Shmuel 1, 6:19), who peeped inside the Aron and died. Indeed, Moshe was careful not to look at the Shechinah, when he saw the Burning Bush.
Why did Hashem not punish them?
Rashi #1: He did not want to disturb the Simchah of Matan Torah. 1
Ramban: Because they obeyed the command not to break their ranks to ascend to Hashem 2 . They looked, but remained in their places.
Rashbam: Due to the covenant into which they had entered, Hashem graciously overlooked their sin and appeared to them. 3
Seforno: To allow them to fully absorb what they had seen.
He did punish them later however - Nadav and Avihu died on the day the Mishkan was inaugurated (which was Hashem's Simchah and not Yisrael's [Vayikra 10:2]), and the elders, in Bamidbar (11:1), at Tav'eirah, when Yisrael grumbled about the incessant travelling (Rashi).
What did they eat and drink?
Rashi #1: The Simchah over the acceptance of their Korbanos was as if they ate and drank. Refer to 24:11:151:1-2.
Rashi (in B'rachos 17a): They were satiated from the radiance of the Shechinah, as if they had eaten and drunk. 1
Seforno: They made a party to celebrate the level that they had reached.
Rashbam: They sacrificed the Olos and ate the (Basar of teh)Shelamim..
Ramban, Moshav Zekenim citing the Rosh: Just as Shelamim in the era of the Beis-Hamikdash were eaten in Yerushalayim (Zevachim, 55b) and in the era of Shiloh, wherever one could see Shiloh (Ramban).
QUESTIONS ON RASHI
Rashi writes that their Simchah was as if they ate and drank. Can one compare such a spiritual beholding of the Shechinah to eating and drinking?!
Pnei Yehoshua (Brachos 17a): The sustenance of one's 248 limbs and 365 sinews is mainly through eating and drinking. So too, their 248 limbs and 365 sinews were purified through Kabalas ha'Torah 1 and its 613 Mitzvos.
R. Chaim Tzvi Fogel: One who eats and drinks, it becomes part of his body. Also here, the Simchah became fixed in them.
He explained Rashi there. However, here Rashi said that the Simchah was due to the acceptance of their Korbanos! (PF)