What did Hashem mean when He said "Lech Alei mi'Zeh"?
Targum Yonasan: He was ordering Moshe to take the people away from the location of the sin, before He destroys them in His anger, 1
Why did Hashem instruct Moshe to "go up to the land"?
Rashi #1: Because Eretz Yisrael is higher than all other lands.
Rashi #2: Seeing as, when He was angry with Yisrael He ordered him to go down, 1 now that He had 'forgiven' them, He ordered him to go up again.
Why did Hashem refer to the people as "ha'Am" and not 'Amcha', like He did earlier (in 32:7)?
Because earlier He was referring specifically to the Eirev Rav, 1 whom Moshe had personally taken out of Egypt, whereas here He was referring to Yisrael as a whole, whom Moshe had taken out of Egypt in his capacity as Hashem's Shali'ach.
Why did Hashem refer to the Shevu'ah that He made to the Avos?
Moshav Zekenim: The plague helped atone for their sin, so now He mentions Z'chus Avos, which will enable Him to fulfill the Shevu'ah