Which tent did Moshe move? Where did he move it to?
Rashi and Targum Yonasan: He moved his own tent to a distance of two thousand Amos (one Mil) outside the camp.
Da'as Zekenim and Hadar Zekenim: 'Ohel' refers to the crowns removed from Bnei Yisrael, which were given to Moshe (Shabbos 88a), as a result of which his face radiated.
Da'as Zekenim and Hadar Zekenim: See answer #2. Some commentaries say that "Ohel" is an expression of light.
Why did Moshe move his tent outside Machaneh Yisrael?
Rashi and Rashbam: Because he held 'Menudeh le'Rav, Menudeh le'Talmid' (If Yisrael are excommunicated from Hashem, then they are also excommunicated from Moshe). 1
Ramban: Because, following the preceding Pesukim 2 - which took place on the ninetenth of Tamuz, he saw that Yisrael's relationship with Hashem was flawed, so he moved his tent until it was repaired when the Mishkan was erected on Rosh Chodesh Nisan. 3
Targum Yonasan: Refer to 33:7:3:3.
Hadar Zekenim (citing R. Yosef Karo): The forty days that he Davened for Yisrael, that is where he was. He did not ascend to receive the second Luchos until Rosh Chodesh Elul. 4
Sanhedrin, 110a: The people all warned their wives (Sotah) against being secluded with Moshe, 5 so Moshe moved his tent outside the camp to counter the suspicion. 6
Because Hashem did not want to speak with Moshe in the Camp (Rashbam).
After ascending Har Sinai on the eighteenth of Tamuz, Moshe descended immediately to report to Yisrael - and spent the middle forty days until Rosh Chodesh Elul in the camp (See Ramban, who establishes the table of events according to the Pesukim from 32:31 until here - Refer also to 32:30:8:1, 2 and see Rav Chavel's footnotes here, DH 'Mem Yom ... ').
The Ramban himself asked on Rashi that after Yom Kipur, Hashem was reconciled with Yisrael! We must therefore say that, since Moshe already fixed the Ohel Mo'ed to speak with Hashem, he continued to go there even after they were reconciled (PF).
Refer to 33:11:3.1:2 and note.
Based on the Pasuk in Tehilim, 106:16 "Vauekan'u le Moshe ba'Machaneh."See Torah Temimah, note 3.
See Torah Temimah, note 3 DH 'mi'Churz la'Machaneh' and DH 've'NIr'eh'.
Why did he call it 'Ohel Mo'ed'?
Rashi and Targum Onkelos: Because it was the meeting-place for whoever wanted to study Torah.
Seforno: Because that is where Hashem met with Moshe - and not in Machaneh Yisrael.
Targum Yonasan: Whoever sinned and did Teshuvah wholeheartedly, would make his way there, confess his sin and Daven that his sin would be forgiven.
Seeing as the people wanted Moshe, why does the Torah write "Mevakesh Hashem"?
Rashi: To teach us that seeking the presence of a Talmid-Chacham is akin to seeking the presence of Hashem.
Targum Onkelos: Because it is referring to people who came to seek teaching from Hashem (whose Shali'ach Moshe was).
Targum Yonasan: Because it is referring to the people who did Teshuvah on their sins, and who came to confess their sins and to Daven to Hashem.
Oznayim la'Torah: This hints at the Midrash that, from the time that Moshe broke the Luchos, One will only be able to learn Torah with difficulty, with suffering and moving from one place to another. 1
See Oznayim la'Torah.
