Why is the verse in Arame'ic?
Rashi: Yirmeyah sent a letter to Yechanyah in exile - it is an answer to the Babylonians, if they will tell Yisrael to serve idolatry. Radak - Hashem told him to send it. They will answer the Bavliyim in their language. Even the command to Yisrael [to say so to the Bavliyim] is in Arame'ic, lest the verse be partially in Hebrew and partially in Arame'ic.
Why does it say "Lehom"?
Radak: Sometimes Lehon (to them) has a Mem at the end, e.g. "Amrin Lehom" (Ezra 5:3), even though usually it has a Nun at the end.
Is "Eleh" Hebrew?
Radak: It is Hebrew and also Arame'ic, e.g. "El Manaya" (Ezra 5:15). It is written there Eleh, but pronounced El. These are the same, e.g. "ha'Aratzos ha'El" (Bereishis 26:3-4). It says Eleh because people see [Shamayim], even though it is high (far away).
What is "v'Arka"?
Radak (from Bereishis Rabah 13:12): It is the land. Chazal say that it is called four names - Eretz, Tevel, Adamah and Arka - corresponding to the four seasons.
What is our answer why will we not serve idolatry?
Targum Yonasan: The gods that you serve have no power. They cannot bring rain from Shamayim, and not make Peros sprout from the earth. They and their worshippers will perish from the land and from below this Heaven. Radak - the answer continues until the end of verse 16. We will not serve gods that did not make Heaven and earth, only Elokim, who made the land with His power. [Yisrael] will understand [the rest of] the answer (verses 12-16), which is in Hebrew, and tell the Bavliyim in Arame'ic. However, the beginning Yirmeyah sent in Arame'ic.
Malbim: Since you agree that Hashem created Shamayim va'Aretz, how can you call idols 'gods'? They did not create anything! If you will say that they created other worlds, they did not create this Shamayim va'Aretz - why are they here, in a world that is not theirs? They will be lost from it!
Yisrael served idolatry in Eretz Yisrael. Did not they not serve in Bavel?
Radak: They did not serve after they were exiled. They bowed to the image that Nebuchadnetzar erected due to Ones. Even so, they were punished (for they should have refused, even if they would be killed) in the days of Haman, if not that Hashem had mercy on them. Chazal said (Megilah 12a) that Yisrael of that generation were worthy to be destroyed because they bowed to the image.
