Why does Moshe's name not appear in the entire Parshah, as it does in every other Parshah in the Torah from the time that he was born?
Rosh, Moshav Zekenim, Ba'al ha'Turim (citing the Zohar): Because he asked Hashem to erase him from the Torah (See Ki Sisa, 32:32) and the curse of a Chacham always materializes (at least in part).
And it is to demonstrate Moshe's sadness that the Torah omits his name from the entire Parshah. See Oznayim la'Torah DH 've'Atah Tetzaveh, #2.
A Z'chus that he lost during the episode of the burning bush, when, for seven days, he refused to become Hashem's emissary.
See Oznayim la'Torah's objections to this explanation DH 've'Atah Tetzaveh, #1. See also DH 've'Atah Tetzaveh, #3, as to why Chazal fixed this Parshah specifically on the day that Moshe was both born and died. Refer also to 27:20:1:5:1.
Why did Chazal pick Tetzaveh as the Parshah to omit Moshe's name?
Oznayim la'Torah: Because it contains the Parshah of the Bigdei Kehunah, and, as the Gemara states in Yoma, 72 , the Bigdei Kehunah enable Yisrael to exist in spite of the sin of the Golden Calf. Consequently, now that Yisrael were only pardoned on the merit of Moshe, who asked for his name to otherwise be removed from the Torah. It is befitting to pick the Parshah which deals with the Bigdei Kehunah to omit Moshe's name, so that the Bigdei Kehunah stand in place of Moshe Rabeinu, who shields over them in all the remaining Parshiyos of the Torah. 1
See also Oznayim la'Torah, DH 've'Atah Tetzaveh' #2, where he gives another answer to the question.
Why did Hashem say "Tetzaveh" in the future"
Rashi (in Emor): The Mitzvah of kindling the Menorah is primarily taught in Emor, 24:2. The Pasuk here is merely explaining the purpose of the Menorah.
Rashbam and Seforno (in a commenting similarly on the expression "Veyikchu Eilecha" [in the future]): Hashem is instructing Moshe here that, when the oil that they donated in Terumah runs out, they should donate fresh oil to continue with the Mitzvah. 1
Rashbam: Because, unlike the issues dealt with in Terumah, the current Pasuk was not a once off donation for the Mishkan, but an ongoing obligation 2 to donate oil for the Menorah once a year.
Why did Hashem use the expression "ve'Atah Tetzaveh" instead of "ve'Asisa" like He constantly did in Terumah?
Ramban #1: Because there was no way that the people could produce in the desert oil that was 'Zach'; It had to have been prepared beforehand and was now brought to Moshe 1 to check (for "Zach" and "Kasis"). 2
Ramban #2 and Seforno: Because, whereas "ve'Asisa" implies via somebody else, Hashem said "ve'Atah here, because he wanted Moshe to personally issue Yisrael with the instruction on manufacturing the oil, 3 bearing in mind that the actual production of the Begadim was performed by Betzalel. 4
Perhaps it is because Moshe's name is not mentioned in the Parshah 5 that the Torah stresses a number of times "ve'Atah", to emphasize that ultimately, everything that took place in the Mishkan was under his auspices. (EC)
Ba'al ha'Turim: An expression of Tzivuy is to make people zealous. It is used for matters that involve monetary loss, such as oil and lambs for the Menorah and Tamid, which apply every day. 6
Rashbam: "Tzav" always means that the Mitzvah is to last for all generations - in this instance, it entails donating fresh oil every year.
Moshav Zekenim: It says "v'Atah", like "v'Atah Es Brisi Tishmor", to hint that on the day of Bris Milah, the father should light Neros, for he is like a Kohen Gadol.
In fact, the Ramban adds, it was the princes who brought it.
Which explains why the Torah writes "Eilecha" (Ramban).
And it is for the same reason that Hashem will shortly use the same expression in 28:1, with regard to bringing Aharon and his sons close - to personally inaugurate them, and with regard to instructing the wise-hearted men the details of manufacturing the Bigdei Kehunah, in 28:3 [Ramban and Seforno]) - because he knew the exact task that each person was capable of performing (Ramban). Refer also to 28:3:1:2 & 28:3:1:3.
As the Torah states in Ki Sisa, Sh'mos, 31:2 (Ramban).
What are the connotations of "Zach" and "Kasis"?
Rashi: "Zach" means pure
How does one obtain good quality oil that falls under the category of "Zach"?
What are the implications of "Kasis la'Ma'or"?
Rashi: It implies "Kasis la'Ma'or", 've'Lo la'Menachos' - the olives may be ground for the oil for the Menorah..
Why did Hashem not also order the Menachos to be 'Kasis'?
Menachos, 86b: Because of the expense involved
See Torah Temimah, note 27.
Why does the Torah use the word "Leha'alos Ner Tamid" rather than 'Lehadlik'?
Rashi: Because the Kohen who lit the Menorah was obligated to apply the lighter until the flame was rising by itself. 1
Yerushalmi, Sukah, 5:3 The Chachamim assessed that the only wicks that perform this task are those made of linen.
What are the connotations of "Tamid" with regard to the Menorah?
Rashi: It means every night. 1
Toras Kohanim (at the end of Emor): "Tamid", 'even on Shabbos', "Tamid", 'even be'Tum'ah' (if the majority of the Tzibur are Tamei). 4
Rashi: In similar vein to the Olas Tamid (in Pinchas, Bamidbar 28:6) where it means daily, to the Minchas Chavitin of the Kohen Gadol (in Vayikra 6:13), where it means half each morning and half each afternoon; as opposed to the "Tamid" that is written by the Lechem ha'Panim (in Terumah, 25:30), where it means that they had to be on the Shulchan from Shabbos to Shabbos.
See Ramban, who elaborates on the definition of 'Ner ha'Ma'aravi'.
In fact, if the Kohen discovered that it had gone out, he was obligated to re-kindle it (Ramban, citing the Sifra in Vayikra, 24:2).
Torah Temimah: This ruling extends to all Korbanos that have a fixed time.
Why did Hashem see fit to precede the Parshah of the oil for the Menorah before that of the Kohanim performing the Avodah?
Oznayim la'Torah: So that the Kohanim should not have to work in the dark. 1
Why did Hashem say "Eilecha"?
Moshav Zekenim: This hints that Hashem does not need the light. 1 It says so also about Parah Adumah, which [was not for Hashem's need, rather,] for Taharah from Chet ha'Egel.
Oznayim la'Torah: Hashem said "Eilecha", both here and at the beginning of Chukas, in connection with the Parah Adumah, in order to console Moshe, who did not have a direct hand in their preparation.
Rashi (citing Menachos, 86b): writes "Kasis la'Ma'or", but not for Menachos. It says below (29:30) "Kasis" for Minchas Nesachim of the Tamid!
Moshav Zekenim: Rashi does not disqualify Kasis for Menachos, only he teaches that it need not be Kasis. What source would we have to require Kasis for Menachos? It was not taught twice to make it obligatory! 1 Rather, "la'Ma'or" is extra (it says "Leha'alos Ner"); it is as if the commanded was repeated, so it is Me'akev. La'Ma'or also excludes Menachos, lest we learn from a Gezeirah Shavah "Kasis-Kasis" that it is Me'akev. (For Menachos it is only l'Chatchilah.)