Why does the Torah write "Kol asher Tzivah Hashem es Moshe, rather than "Kol asher Tzivah oso Moshe"?
Rashi and Ramban (citing Yerushalmi Pe'ah, 1:1): Because Betzalel did even what Moshe did not tell him - in that Moshe instructed him to manufacture first the Keilim and then to construct the Mishkan, whereas Betzalel reversed the order, 1 just as Hashem had instructed Moshe.
See Tosfos, Berachos, 55a.
Rashi writes that Hashem told Moshe to make the Mishkan first, and Moshe told Betzalel to make the Kelim first. Why did he do so?
Maharam Shik (Brachos 55a): Moshe was not conveying the order of which to make first. He mentioned the Aron first because the Torah inside it is primary, to teach people the path to go in. Betzalel said that presumably, the Aron is the purpose, but we need not make it first - 'Sof Ma'aseh b'Machshavah Techilah'! Moshe replied, you understood the purpose of the Mishkan; this was my intent.
Tosfos (Brachos 55a): Moshe relied on Parshas Terumah, in which Hashem first commanded about the Aron, even though in Ki Sisa, He commanded first about the Mishkan.
Why does the Torah write that Betzalel did everything ... ?
Ramban: It is not to preclude the wise-hearted men who worked together with him. 1 It is to point out that Betzalel not only taught them what to do, but that he also oversaw every aspect of the building and that the workers brought him everything that they did for inspection.
See 36:8 (Ramban).
Rashi writes that Moshe told to Betzalel to make the Kelim first, and Betzalel reversed the order. Why did he do so?
Rashi, citing Berachos 55a: Betzalel argued, it is customary (and logical) to first build the house and then to place the Keilim inside it; to which Moshe replied [your name alludes to] "b'Tzel Kel Hayisa!" - 'You were in the shadow of Hashem!' This is precisely what Hashem told me. 1
Hadar Zekenim (36:8): This was for the honor of the Aron, so when they make it, they will immediately have where to put it.
Ayeles ha'Shachar: In any case the Mishkan will not be erected until Nisan, so the order should not matter. The Kelim atone for Yisrael, so Moshe thought that it is proper to make them first. Betzalel understand that they atone only after there is a Mishkan and the Shechinah dwells in it.
Ner Uziel (p. 476): Hashem created the world for His honor (Yeshayah 43:7, Avos 6:1). This is fulfilled when He is able to bestow His good to all His creations (Da'as Tevunos 128, Ru'ach Chayim Avos 1:3, DH v'Na'amik). The Mishkan is a dwelling for the Shechinah; we build it for Hashem's honor. Through the Kelim, Yisrael get Kaparah and reward. Hashem commanded Moshe first about the Kelim. Betzalel understood that Hashem shows precedence to man's reward - but we should show precedence to Hashem's honor 2 , and build the Mishkan first! Moshe understood that Hashem wanted that we come to realize this.
Refer to 38:22:2:1.
Tosfos (55a): In the actual command to build, in Ki Sisa (Perek 31), He commanded first about the Mishkan. (Parshas Terumah taught what they will make, but it is not the actual command. - PF)
Ner Uziel: The Mishkan also honors Yisrael, that the Shechinah will dwell among us. Resting on Shabbos testifies that He created the world, and honors Him. Hashem commanded Moshe about the Mishkan before Shabbos (at the beginning of Ki Sisa), but Moshe commanded Yisrael about Shabbos first (at the beginning of Vayakhel). (The author also pointed out that the Torah says "Chag ha'Matzos" (from which we get reward), and we call it Pesach, to recall the mercy and miracle that Hashem bestowed on us. - PF)
Why does the Torah write Betzalel's lineage three times?
Moshav Zekenim: This corresponds to three attributes in him - gifts that he had - Chachmah, Tevunah and Da'as.