What is the significance of the words "ha'Menorah ha'Tehorah"?
Rashi #1: It indicates that the Menorah was made of pure gold. 1
Rashi #2: It teaches us that the Kohen had to place the oil for lighting on 'Tiharah Shel Menorah' (the Menorah itself), and not on the ashes - which had therefore to be removed first.
Ramban (on Pasuk 2, citing the Sifra): It teaches us that the lamp-holders needed to be placed on 'Tiharah Shel Menorah' (the Menorah itself), and not supported with small pieces of wood or stones. 2
Menachos, 29a: It teaches us that Moshe was shown the image of the Menorah that came down from Heaven.
Oznayim la'Torah: Refer to 24:2:1.1:1 and note.
Why does the Torah insert the words "Lifnei Hashem"?
Ramban: To teach us that Aharon should arrange the Neiros in the Menorah in their correct location in the Heichal, and not outside, and bring the Menorah in afterwards. 1
See Torah Temimah, note 5.
Why does the Torah repeat the word "Tamid"?
Sifra: "Tamid" - 'even on Shabbos'; "Tamid" - 'even be'Tum'ah'. 1
Oznayim la'Torah: Based on the principle 'Ein Ribuy achar Ribuy Ela le'Ma'et', 2 the Torah inserts "Tamid" three times - here in Pesukim 2, 3 & 4; Once (in Pasuk 3), for the Mitzvah to kindle the lights every night; once (in Pasuk 2), to prelude the Ner Ma;araviz, which burned - when they were meritous - all night and all day; 3 and once (in Pasuk 4), where the Torah writes "Lifnei Hashem to preclude when they traveled from the obligatqion to light the Menorah every night.
Refer to Sh'mos, 27:20:7:3*.
As opposed to the Lechem ha'Panim, where the Torah writes only once "Tamid", and where there are therefore no exceptions. See Oznayim la'Torah, citing the Rambam.
Which explains why the Torah writes "Ner" (singular) and not 'Neiros' (Oznayim la'Torah).