What is "Lo Sa'asun Iti" referring to?
Rashi and Targum Yonasan and Avodah Zarah, 43b: It means that one may not make an image of any of the celestial bodies that serve Hashem in the Heaven. 1
Ramban #1: The Torah is issuing two prohibitions; 1. against making images to assist Hashem (Lo Sa'asun Iti ... "); and 2. against making images per se (Lo Sa'asu lachem"). 2
Ramban #2 (according to Kabalah): It is synonymous with "Al Panai". 3
Seforno: The Pasuk is issuing a prohibition against making silver or golden gods to act as intermediaries to come closer to Hashem.
Avodah Zarah, 43b: All forms are permitted except for that of man, because "Iti" is akin to 'Osi'. 4
Mechilta (citing R. Akiva): 'Do not do to Me what others do to their gods - When things are going well they bless them and when they are going badly, they curse them; You should give thanks to Hashem both for the good and for the bad! 5
Oznayim la'Torah: It is referring to the 'Arba'ah Panim she'be'Merkavah' (the four faces 6 that support Hashem's Throne). 7
Targum Yonasan and Avodah Zarah, 43b: Incorporating the sun, the moon, the stars, the Mazalos and the angels - the Ofanim, the Serafim or the Chayos ha'Kodesh - Avodah Zarah, Ibid).
As the Torah writes in Vayikra 26:1 (Ramban).
And the Torah wrote in Bereishis, 1:27 "be'Tzelem Elokim Bara oso" (Torah Temimah).
See Torah Temimah note 104 citing the conclusion of the Mechilta.
'D'mus Adam, D'mus Shor, D'mus Aryeh and D'mus Nesher' that support Hashem's Throne.
Oznayim la'Torah: Until now, they had only seen the celestial hosts that dwell in the lower Heavens, which the Torah forbade to worship in the Aseres ha'Dibros. But now that they had seen the 'four faces' ('Arba'ah Panim she'be'Merkavah') that dwell in the upper Heavens, Hashem issued an additionsal La'av, incorporating in the Isur the four faces, the Serafim, the Ofanim and the Chayos ha'Kodesh that thye Mal'achei ha'Shareis that serve in the upper Heavens.
Having written "Lo Sa'asun Iti", why does the Torah add "Elohei Kesef ... "?
Rashi It is a prohibition against making the Keruvim (on the Aron ha'Kodesh) out of silver. 1
Ramban: Refer to 20:20:1:2.
Sanhedrin, 7b: 'Since when are wooden gods permitted? The Pasuk must therefore be referring to judges 2 who are appointed for silver and gold (by paying bribes).
Why does the Torah add "v'Elohei Zahav"?
Rashi: This is an additional prohibition against manufacturing four Keruvim, instead of two.
What is "Lo Sa'asu lachem" coming to include?
Rashi: And this adds a prohibition against making Keruvim in the Batei Kenesiyos and in the Batei Midrash - (like the Keruvim in the Beis-Hamikdash - Mechilta).
Ramban: Refer to 20:20:1:2.
What is the underlying reason behind these prohibitions?
Ramban #1 (in Pasuk 21, citing the Ibn Ezra): Because Hashem wants us to worship Him directly, not via intermediaries. 1
Ramban #2 (citing the Mechilta): The Torah is instructing us here that, when constructing a Mizbe'ach of earth or of stone -in Pasuk 22 - one should construct it in the Mishkan and in the Mikdash in the Name of Hashem, and not in the field in the name of the demons. 2
Because, wherever we mention His Name, He will come and bless us, in which case intermediaries are superfluous (Ramban). Oznayim la'Torah on Pasuk 19, based on the Rambam in the first chapter of Hilchos De'os: To counter the people in the generation of Enosh who believed that, since it was below Hashem's dignity to run the world personally, He appointed the celestial hosts to do so on His behalf - which eventually led to their worshipping the images of those celestial hosts. Therefore Hashem spoke to us directly from the Heaven, to demonstrate that we had now come directly under His jurisdiction and had no need of intermediaries. See Oznayim la'Torah, who clarifies the difference between Yisrael and the Nochrim in this regard.
As they had been accustomed to doing in Egypt. See Rashi, Vayikra 17:5.