Why did Moshe kneel and prostrate hinself?
Rashi and Rashbam: When he saw the Shechinah passing and heard its voice. 1
Seforno: Out of submission to Hashem who was passing.
Moshav Zekenim: It refers to 33:14, when Hashem said "Panai Yeleichu ...". Moshe bowed as a sign of gratitude 2 - like one who received a great gift from the king, and he thanks and bows down to him. 3
Da'as Zekenim (in Pasuk 7) and Hadar Zekenim: After hearing that Hashem is "Rachum ve'Chanun", he was no longer afraid ("Pen Achelcha ba'Darech"), so he thanked Hashem bowed and continued to Daven.
Sanhedrin, 111a: Because he 'saw' the Midah of "Erech Apayim". 4
Either in awe of the Shechinah or in submission to it.
Moshav Zekenim: Since an angel would not pardon our sins, but Hashem, who is full of mercy, will.
If Hashem promised to go among us, why, in the following Pasuk, does Moshe repeat the request? This is difficult even according to the other explanations - that Moshe prostrated himself after he heard the thirteen Midos. Refer to 33:15:1:3 & 4 and to 34:9:1:1-3.
See Torah Temimah, note 16.
What is the significance of the fact that Moshe hurried to kneel and prostrate himself?
Seforno: It is a sign of total submission, demonstrating the esteem in which one holds the one before whom one is prostrating oneself. 1
Moshav Zekenim #1, Da'as Zekenim (in Pasuk 7) #1 and Hadar Zekenim #1: He was afraid that Hashem would add more generations, and that everyone would subsequently stumble in the sins of his fathers (and be punished for them). 2
Rosh: He was afraid that Hashem would pass quickly. 3
See Torah Temimah, note 16.
As the Gemara relates in B'rachos 12b - when Rav Sheishes would bow down, he would bow down like a stick - in one quick motion, and unfurl like a snake (Seforno).
If Hashem's Midah were to punish until the fifth generation, would Hashem change His Midos because Moshe bowed? (PF)
Rosh: As the Navi writes in Yirmiyah 4:13 "ve'Chasufah Markevosav" (His chariots are swift).