Why does the Torah issue the warning specifically here?
Rashi: Because it is when a person is satiated, he tends to lash out and rebel against Hakadosh-Baruch-Hu, as the Torah wrote above. 1
What does "Vesartem" refer to? What is the connection with the continuation of the Pasuk?
Rashi: It refers to the way of Torah and Mitzvos, and the Torah is teaching us that, once you stray from the path of Torah and Mitzvos, you will worship other gods and cling to them. 1
Rashi: As David ha'Melech said in Shmuel 1, 26:19 "For they drove me away from clinging to the inheritance of Hashem (from Torah-study) saying 'Go and worship other gods!', because once a person is exiled from studying Torah, he is but one step away from worshipping idols. Lev Eliyahu (Shemos p.92)
What are the implications of "Elohim Acherim"?
Refer to Shemos, 20:3:3:1, 2 and the notes there.
Why does the Torah mention enticement of the heart?
Lev Eliyahu (Shemos p.91): Enticement applies to only to the heart, i.e. emotion. When the heart is blunted, lust overpowers, and intellect cannot stand against it at all, and a person comes to idolatry.