Having already stated the Parshah of the Neiros at the beginning of Tetzaveh, why does the Torah repeat it here?
Rashi #1: In fact, this is the main Parshah of the Neiros, and the one in Tetzaveh is secondary. 1
Rashi #2 (in Machzor Vitri): The Torah inserts it here after the Mo'ados, as a hint for Chanukah. 2
Ramban #1, Moshav Zekenim #1 and Seforno: Because the oil that the princes originally donated had run out; the Torah is therefore teaching that the Tzibur needs to donate more oil for the future, and that it must be manufactured in exactly the same way as the original oil.
Ramban #2, Moshav Zekenim #2: It also comes to teach us that the Menorah is crucial to the Mitzvah of Hadlakas Neiros. 3
Rashbam: It mentions it here because the basic objective of the Menorah was to illuminate the Shulchan, whose Lechem ha'Panim the Torah is about to discuss.
Moshav Zekenim: It is written after the Mo'ados, to teach that lighting Ner Shabbos is a Mitzvah. This is the source for Ashkenazim to bless on Ner Yom Tov 4 , just like on Shabbos.
Moshav Zekenim citing R. Yehudah ha'Chasid: It is written after Sukos, to teach that during Chanukah we decrease the number of Neros each night, just like the number of bulls in Musaf decreases every day of Sukos. Beis Hillel learn from Lechem ha'Panim, written after [the Neros], about which it says "b'Yom ha'Shabbos" (verse 8); we increase from Chol onto Kodesh, (each day we add to the number of Neros, which are Kodesh) just like we do on Shabbos (we cease Melachah before Shabbos actually comes).
Moshav Zekenim: There is a hint to Purim, for it is next to the Mekalel, and Haman said "Kol Zeh Einenu Shavah Li." Everyone stoned 5 is hung; also Haman was hung.
Ba'al ha'Turim: It is written after Sukos, to teach that we complete Hallel during Chanukah, just like during Sukos.
Rashi: Hence the Torah here writes "Tzav es Bnei Yisrael", whereas there it writes "v'Atah Tetzaveh ... ", as if to say that 'You will later command Yisrael' - with reference to here.
Which lasts eight days like Sukos which precedes it.
Ramban, Moshav Zekenim: As the Torah indicates in Pasuk 4 - despite the fact that, at the beginning of Tetzaveh, the Pasuk implies that one is permitted to kindle the lights without a Menorah, in the event that the Menorah is lost or broken - as occurred when they returned from Galus Bavel.
Moshav Zekenim: Chachamim of France disagreed. The Chiyuv of Ner Shabbos is due to Shalom Bayis. One may light on Yom Tov, so there is no need to light beforehand due to Shalom Bayis, therefore one does not bless. R. Tam held that one does not bless even on Ner Shabbos, since it is only due to Shalom Bayis.
Why did he need to say so, like R. Eliezer? Chachamim agree that a Megadef is hung (Sanhedrin 45b), and the Halachah follows them! (PF)
What are the connotations of "Shemen Zayis Zach"?
Rashi: Three different kinds of oil are produced from the olive, and it is only the first that is eligible for the Menorah.
What are the implications of the word "Tamid"?
Rashi: "Tamid" in this context means every evening. 1
Ramban: Refer to Shemos, 27:20:7:2.
Why does the Torah use the expression "Leha'alos Ner Tamid"?
Rashi: Refer to Shemos, 27:20:6:1.
Ba'al ha'Turim: This is a support for Beis Hillel, who say that during Chanukah, the number of Neros we light to fulfill the bigger Hidur) increases each night.
Why does the Torah say "Tzav" here?
Rashi (6:2, citing R. Shimon): Because encouragement is particularly crucial when there is financial loss. (The Tzibur pays for oil to burn every night, and Kohanim do not benefit from it.)
Moshav Zekenim: "Tzav" is often written when there is financial loss, and rarely written when there is no financial loss.
Why does it say to take the oil "Elecha"?
Moshav Zekenim: When Hashem commanded about the Menorah, Yisrael said 'I know that You do not need the light. You command so only to bring merit to us!' Hashem says, illuminate for Me in this world, and I will illuminate for you in the world to come - "Hashem Yihyeh Lach l'Or Olam" (Yeshayah 60:20). Light in the Kodesh place brings salvation - "Hashem Ori v'Yish'i" (Tehilim 27:1).