What are the connotations of "uv'Chol Asher Amarti Aleichem Tishameru"?
Rashi #1: It adds a Lo Sa'aseh to every Asei. 1
Ramban: With reference to the following phrase, the Torah is warning us here to strictly adhere to all the warnings concerning Avodah-Zarah, 2 and that moreover, one may not even mention their names 3 either personally, or cause them to be mentioned by their adherents.
Seforno: With reference to the following phrase, the Torah is warning us here although one needs to take care not to transgress any of the Mitzvos of the Torah, 4 when it comes to Avodah-Zarah, one needs to take additional care even not to mention its name.
Rashbam #1: The Torah is reiterating here, all the Mitzvos that it presented since the beginning of the Aseres ha'Dibros until now.
Rashbam #2 (citing Shabbos, 18a): It is coming to add Shevisas Keilim (not allowing our vessels to work for us on Shabbos). 5
Rashi #2: The Torah is teaching us here that idolatry (mentioned right after this) is on a par with all other Mitzvos combined. 6
Da'as Zekenim (12) #1: Even though I commanded you about [not afflicting] a Ger, do not join with him too much.
Da'as Zekenim (12) #2: After this, the Torah commands about the festivals, i.e. times of Simchah. One is prone to speak improperly amidst wine or intoxication - therefore, it says 'guard everything I commanded!' Know Hashem in all your ways!
Based on the principle 'Hishamer, Pen and Al are Lo Sa'asehs. See Sifsei Chachamim and Ramban. Citing Eruvin, 96a, the Ramban concludes that 'Hishamer of an Asei is an Asei'. See Rashi Devarim 13:1.
Not to worship them or bow down to them, to annihilate those who worship them, not to make a like image or a picture of them. (Ramban).
Ramban: E.g. Kemosh, god of Mo'av, Malkom, god of Amon and Asima, god of Chamos - even without mentiong the word 'god'. (Why does the Ramban list idolatries mentioned in Tanach? Sanhedrin 63b permits mentioning them! - PF)
This also appears to be the way Targum Onkelos and Targum Yonasan explain the Pasuk.
See Shabbos, 18a.
Rashi: One who transgresses it, it is as if he transgressed all the Mitzvos, and conversely for one who is careful about it. See also Ba'al ha'Turim.
What does "ve'Shem Elohim Acherim lo Sazkiru" mean?
Rashi #1: It is a prohibition against mentioning the name of an idol, even as a landmark. 1
Ramban: Refer to 23:13:1:2.
Seforno: Refer to, 23:13:1:3.
What are the connotations of "Lo Yishama al Picha"?
Rashi and Ramban (citing Sanhedrin, 63b) #1: It is a prohibition against entering into a partnership with a Nochri, thereby causing him to swear by the name of his god, should a disagreement between the partners occur. 1
Ramban #2: One may not enter into a partnership with a Nochri in case one mentions the name of one's partner's god, to say to him, 'Do me a favor in the name of your god!', or in some other way. 2
Seforno: It is a prohibition against others mentioning the name of their god, with our consent.