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, to instuct Moshe details concerning the Menorah in anticipation of the Mitzvah here. 1
Rashi #2 (in Machzor Vitri): The Torah inserts it here after the Mo'ados, to hint at Chanukah, 2
Ramban #1, Moshav Zekenim #1 and Seforno: Because the oil that the princes originally donated had run out, and the Torah is therefore informing the Tzibur that they need to donate more oil for the future, and that it must be manufactured in exactly the same way as the original oil.
Ramban #2 and Moshav Zekenim #2: It 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 discusses immediately afterwards.
Moshav Zekenim: It is written after the Mo'ados, to teach us that lighting Ner Shabbos and Yom-Tov is a Mitzvah. This is the source for Ashkenazim to recite a B'rachah over Ner Yom Tov just like on Shabbos. 4
Moshav Zekenim #2 citing R. Yehudah ha'Chasid: It is written after Sukos, acording to Beis Shamai?to teach us that during Chanukah we decrease the number of Neiros each night, just like the number of bulls in Musaf decreases every day of Sukos. 5
Moshav Zekenim: #3 There is a hint to Purim, for it is next to the Mekalel, and Haman said "Kol Zeh Einenu Shavah Li." Everyone stoned 6 is hung and Haman too was hanged.
Ba'al ha'Turim: It is written after Sukos, to teach us that we complete Hallel during Chanukah, just like during Sukos. 10: Oznayim la'Torah: Because, having omitted Moshe's name in Tetzaveh, the Torah repeats it here in order to add his name to the command. 7
Rashi: Hence the Torah here writes "Tzav es B'nei Yisrael", whereas there it writes "ve'Atah Tetzaveh ... ", as if to say that 'You will later command Yisrael' - with reference to here.
Rashi (Ibid.): Which lasts eight days like Sukos which precedes it, and is a Yom-Tov like the Chagim (though Melachah is permitted). Se also Oznayim la'Torah, end of DH 'Veyikchu Eilecha ... '.
Ramban and 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: The Chachamim of France disagree, bearing in mind that The Chiyuv of Ner Shabbos is because of Shalom Bayis, and kindling a light on Yom-Tov is permitted. R. Tam mantains that one does not recite a B'rachah even over Ner Shabbos either, since it is only due to Shalom Bayis.
Beis Hillel on the other hand, learn that we add on to the Neiros each day, from the Lechem ha'Panim, which the Torah discusses immediately after that of the Neiros, and about which the Torah writes in Pasuk 8 "be'Yom ha'Shabbos" - and on Shabbos we increase from Chol onto Kodesh by stopping work before Shabbos actully arrives.
Why does the Torah juxtapose the Parshah of Neiros and that of the Lechem ha'Panim to the Parshah of Mo'ados?
Oznayim la'Torah: Because, based on a Bersaisa in Chagigah - that, due to the fact that a. Kohanim Amei-ha'Aretz, who all served in the Beis-Hamikdash on Yom-Tov and who may have touched the holy Keilim, they would Tovel all the Keilim immediately after Yom-Tov; and that. b. bearing in mind that the Torah writes "Tamid" by the Shulchan and the Menorah - which could therefore not be Toveled, they would instruct the Kohanim Amei-ha'Aretz to be careful not to touch them. And this is hinted here by the fact that the Torah juxtaposes the two Parshiyos to that of Mo'ados. 1
And the hint is enhanced by the fact that the Torah uses the expression "ha'Menorah ha'Tehorah" and "ha'Shulchan ha'Tahor", - in Pasuk 4 & 6, respectively - which it does not do by any of the other Keilim. AnD this also explains why the Torah begins Pasuk 3 with "mi'Chutz la'Paroches ha'Eidus" - to stress that the instructions to the Kohanim were only necessary because the Menorah and the Shulchan were placed outside the Paroches, were Kohanim were permitted to serve, but would have been superfluous had they been placed behind the Paroches.
What are the connotations of "Shemen Zayis Zach"?
Rashi: It teaches us that, of the three different lots of oil that the olive produces, only the first one - which is completely refined. is eligible for the Menorah.
What are the implications of the word "Tamid"?
Rashi: "Tamid" in this context implies every evening. 1
Ramban #1 (citing the Sifra) 2 and Targum Yonasan: It means both on Shabbos and during the week. 3
Ramban #2: Refer to Sh'mos, 27:20:7:2.
Why does the Torah use the expression "Leha'alos Ner Tamid"?
Rashi: Refer to Bamidbar, 8:2:3:1-3.
Ba'al ha'Turim: This is a support for Beis Hillel, who say that during Chanukah, the number of Neiros we light (to fulfill Mehadrin min ha'Mehadrin) increases each night, since "Leha'alos" has connotations of increasing.
Why does the Torah insert the words "Tzav es B'nei Yisrael" here?
Rashi (6:2, citing R. Shimon): Because encouragement is particularly crucial when there is financial loss (since a. the Tzibur pays for oil to burn every night, and b. the Kohanim do not benefit from it).
Moshav Zekenim: "Tzav" is often written when there is a financial loss, and is rarely written when there is not.
Why does the Torah insert the word "Veyikchu Eilecha ... "?
Moshav Zekenim: When Hashem issued the command concerning the Menorah, Yisrael said 'I know that You do not need the light that Your command is only in order 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 Yih'yeh lach le'Or Olam" (Yeshayah 60:20). Light in the Kodesh place brings salvation - "Hashem Ori ve'Yish'i" (Tehilim 27:1).
