Who instructed Moshe to ascend Har Sinai?
Ramban: Hashem (mentioned in Sh'mos 20:19) now ordered Moshe to ascend Har Sinai. 1
Rashbam: An angel. 2
Targum Yonasan, it was Micha'el, the angel of wisdom (See Peirush Yonasan). Moshav Zekenim - the letters of "Mal'achi" spell Micha'el 3 , the angel that Hashem sent to lead Yisrael.
Until now, Hashem had been instructing Moshe the Mitzvos and Mishpatim to pass on to Yisrael; now He was instructing him what he (Moshe) himself had to do (Ramban).
Moshav Zekenim: Initially Hashem wanted to send Metatron, the judge; there is no mercy in judgment. Moshe requested an angel of mercy, and He sent Micha'el.
Since Hashem was speaking, why did He say "Alei el Hashem, and not 'Alei Eilai"?
Rashi (in Sanhedrin, 38b): It was Matatron, whose name is synonymous with His Master, instructing Moshe to go up to Hashem. 1
Ramban #1: It is common practice for the Torah to state the name in place of the pronoun. 2
Ramban #2 (citing Sanhedrin, 38b): It was Hashem instructing Moshe to go up to Matatron, whose name is synonymous with His Master. 3
When was this Parshah said?
Rashi: It was said on the fourth of Sivan (before Matan Torah). 1
And on the fifth of Sivan, Moshe built a Mizbe'ach, and they brought on it Olos and Shelamim and entered into a covenant via the blood of the Korbanos (Rashi, Gitin, 88b). See also Sifsei Chachamim. According to the Ramban, this is one opinion in the Mechilta. The Ramban himself explains the Parshah according to the other opinion. Refer to 24:1:3:2.
It therefore transpires that all the Pesukim from Sh'mos 20:19 until 23:33 (known as 'Seifer ha'Beris' are written in the correct order. Moreover, the words of Hashem and the Mishpatim referred to in Pasuk 3 are synonymous with the Aseres ha'Dibros and the Mitzvos of Parshas Mishpatim - and not the Mitzvos of P'rishah and Hagbalah, which were said at Marah, and the seven Mitzvos B'nei No'ach, as Rashi explains there (Ramban). According to the Rashbam, Moshe only ascended after the cloud had covered him for six days (See Rashi in Ki Sisa, Sh'mos 24:16).
Consequently, Pasuk 3 and the first part of Pasuk 4, took place on the same day, and from the second half of Pasuk 4 until Pasuk 11, on the following day, on the seventh of Sivan, when Moshe finally ascended the mountain for forty days (Ramban). It is remarkable that, according to the Ramban, "Na'aseh ve'Nishma" was said after Matan Torah!
If this Parshah was said before Matan Torah, as the Mechilta explains, why did the Torah insert it here and not in Yisro, where it chronologically belongs?
Oznayim la'Torah: Bearing in mind that Moshe ascended Har Sinai in order to receive the Luchos in Pasuk 12, is to preempt the question how Hakadosh-Baruch-Hu could favor them after they worshipped the Golden Calf, when Hashem specifically stated in the Aseres ha'Dibros "Lo Yih'ye l'cha Elohim Achreim" and in 22:19 "Zove'ach la'Elohim Yocharam"? Therefore the Torah states the praise of Yisrarel, who declared earlier "Na'aseh ve'Nishma!"
Why were Elazar and Itamar not told to ascend? They were at a higher level than the Zekenim, like we find in Eruvin (54b)!
Moshav Zekenim: Hashem knew that those who ascended (except for Moshe and Aharon) would be Chayav Misah; the Zekenim 1 died at Tav'eirah. Had also Elazar and Itamar ascended, all of Aharon's children would have died. 2