What is the significance of the words "Rega Echad"?
Rashi: It signifies the moment that Hashem's anger lasts. 1
Seforno: Hashem was telling the people not to mourn the fact that He would remove His Shechinah from their midst. Since they are stiff-necked and do not turn to hear their teachers, if He would be among them, He would consume them in a moment, despite the fact that they acquired preparation for perfection on Har Sinai! 2
What is the connection between the first half of the Pasuk and the second half?
Rashi: Even though Hashem was about to send a Mal'ach, to prevent His Shechinah from destroying Yisrael should they sin, the punishment of the ornaments was to take effect immediately and Hashem had already decided how He would punish them to atone for the rest of the sin. 1
Seforno: Since this demotion was necessary, they should remove their spiritual preparedness 2 that they received at Ma'amad Har Sinai.
Hadar Zekenim: Hashem said, 'Since, due to your stubborness, I planned not to go with you, remove your weapons, 3 until I decide what to do with you - whether to go with you or not'.
And not to destroy them (Rashi in Shabbos, 88a). See also, Bereishis, 18:21:3:1.
Presumably, this refers to the ornaments, as explained by the other commentaries. Refer to 33:4:1:1 & 3.
See Hadar Zekenim, who elaborates.
Why did Hashem instruct the people to remove their ornaments?
Seforno: Because, once Hashem gives a present, He does not take it away without the recipient's consent.
Sha'arei Teshuvah (1:29): Hachna'ah (submissiveness) in action is a part of Teshuvah. Consequently, one should not engage in beauty of clothing or ornaments when performing it. 1
As the Gemara states in Ta'anis, 25a. See Esther, 4:1 & 3, which describes how Mordechai and the people donned sack-cloth and ashes when doing Teshuvah.
What did Hashem mean when He said "ve'Eid'ah Mah E'eseh lach"?
Rashi: Refer to 33:5:2:1.
Seforno: He meant that, once they remove the above-mentioned 'preparedness', they would no longer be subject to such a severe punishment.
Targum Onkelos and Targum Yonasan: He meant that it was revealed before Him what He would do to them.
Moshav Zekenim #1 (citing the Rosh): He meant that He would punish them according to His knowledge, based on their mourning and regret of their sin.
Moshav Zekenim #2: He ment that He would give them Yom Kipur to atone for them.
This is why Moshe said in Pasuk 12 'You did not inform me' (what You decided).
Why did Hashem say "E'eleh (I will ascend) in your midst"?
Rosh: It means the opposite - 'I will descend ... '. 1
Targum Yonasan: It means 'I will remove My Shechinah".
Rosh: And we find that it sometimes refers to descent. See Iyov 6:18 and Melachim 1, 9:8.