Why did Hashem say "Anochi" and "Lo Yih'yeh Lecha ... " in the first person?
Rosh: Refer to 20:1:154:2*.
The Mechilta compares this to a king whose subjects asked him to issue decrees (to form a constitution), and who replied 'First crown me king; then I will issue decrees! - because if you don't accept my sovereignty, you won't accept my decrees either'. Similarly, Hashem said to Yisrael 'I am Hashem your G-d! Do not accept any other gods!', before issuing them with other Mitzvos (Ramban). Refer also to 20:2:2:3.
What does the Lav of "Lo Yih'yeh Lecha" entail?
Rashi #2 (in Vayikra 19:4): Neither your own nor those belonging to others.
Ramban #2, Seforno and Rashbam 3 : It is a prohibition against accepting any deity 4 other than Hashem, even in its capacity as a servant of Hashem 5 (Seforno). 6 One may neither believe in it, accept it as a god, nor declare it as one's god (Ramban). 7
Hadar Zekenim: Do not say 'I will serve Hashem, and also other gods that will help me.' You need only Me, for they are folly and nothingness!
Moshav Zekenim, Pane'ach Raza: Do not think that there is any image of Hashem. Even though it says "b'Tzelem Elokim", there is an Asnachta 8 under b'Tzelem (it is not connected to Elokim). Rather, b'Tzelem (in an esteemed mold that Hashem possessed), Elokim made man.
Since the prohibition against manufacturing them is contained in the next Pasuk (Rashi).
In which case this is a plain Lav that is not subject to Kareis (Ramban). According to the Ramban, the prohibition against retaining an image is an individual opinion.
From among the angels and the celestial bodies - that also bear the title 'Elohim' (as in Shemos 22:19 [Ramban]) - bearing in mind that Hashem took us out of Egypt single-handedly (Refer to 20:2:1:1).
Despite the principle 'Eved Melech ke'Melech' (Shevu'os, 47b).
Rikanti: This is also how the Ramban (in his Kabalistic interpretation), explains Targum Onkelos (Refer to 10:3:4:4* [See Rav Chavel's commentary on the Ramban]).
What are the connotations of "Elohim Acherim"?
Rashi #1: This means that although they are not gods, others made them into gods. 1
Rashi #2: They are strangers to their own adherents, since they do not respond when they call them. 2
Ibn Ezra, according to Moshav Zekenim and Hadar Zekenim: People think that they are gods, but they err.
It cannot be understood literally, since it would be a slight to Hashem to refer to images as 'other gods' (Rashi).
As if they were somebody else - not the one being called (Rashi).
What does "Al Panai" mean?
Rashi #1: It means 'as long as I exist' - in other words, forever.
Rashi #2 (in Devarim 5:7): Wherever I am - in other words, anywhere in the world.
Ramban #1: It means that Hashem is there watching 1 anyone who transgresses, wherever and whenever it may be.
Ramban #2 (according to Kabalah). Targum Onkelos and Targum Yonasan: "Besides Me". 2
Seforno: This is a reason for the prohibition 3 - because one does not pay homage to servants in the presence of their master.
With reference to Micha'el (the Mal'ach ha'Beris) who accompanies Hashem wherever He goes. He is also the Mal'ach who appeared to Moshe at the Burning Bush, and this explains why Moshe bowed down to him there (Ramban). Refer also to 20:3:2:3*****.