What is the Isur of "Molech"?
Rashi, Ramban #1 (citing Ibn Ezra) and Seforno: "Molech" is the name of an Avodah-Zarah. 1
Ramban #4 (in Vayikra 20:5, citing Sanhedrin, 64a): Molech is not an Avodah-Zarah at all, but a form of sorcery.
Targum Yonasan #2: It is a prohibition against desecrating one's son by handing him over in marriage to a Nochris. 4
Probably Malkom, the god of Amon (Ramban). In Parshas Vayikra (20:5) however, the Ramban proves that Molech is an irregular form of worship, which Amon called by that name because he was their king, but which applies equally to any Avodah-Zarah that one worships in this (irregular) way (See Ramban there DH 've'Hinei').
Whereas "Ma'avir B'no u'Bito ba'Eish" (Devarim 18:10) is a form of sorcery, since the Pesukim in Vayikra 20:6, in Devarim (18:10), in Divrei ha'Yamim 2, (33:6) and in Melachim 2, (17:17) all insert it in a list of different forms of magic, and not under the category of Avodah-Zarah (Ramban).
What did the service of Molech entail?
Rashi: The father would hand over his son to the priests who, then arranged two rows of fire and passed the son between them by his legs. 1
Targum Yonasan (in Vayikra 19:2): The father would hand over his son to be burnt in fire.
See Ramban, who queries this explanation from the Gemara in Sanhedrin and as to how the father can be Chayav Misah on an act that somebody else performs.
Ramban: In the same way that the owner of a Korban would hand it over to the Kohanim.
Ramban citing the Yerushalmi): They then performed Tenufah or Hagashah in front of Molech before handing him back to his father.
What makes sacrificing to Molech a Chilul Hashem?
Ramban and Seforno: The Chilul Hashem lies in the fact that one sacrifices only animals to Hashem and one's sons to Molech. 1
As the Pasuk intimates in Yechezkel, 23:37, 38 & 39 [Ramban]). It is also Metamei the Mikdash (as the Torah adds in Vayikra 20:3), which refers either to the desecration of the sanctity of Yisrael, referred to in Vayikra 11:34 ("Metamei" is a term that the Torah uses when it speaks about major sins - See, for example, Amos, 2:7]), or to the desecration of the Beis-ha'Mikdash, when they sacrifice their children to Molech and then proceed to the Beis-ha'Mikdash to bring Korbanos (See Vayikra 19:31 & Yechezkel, 36:18 [Ramban]), or to the sanctity of Hashem, which is contained in his son (as it is contained in every Jew [See Ramban, DH 've'Al Derech ha'Emes]).
Why does the Torah juxtapose the Parshah Molech to that of Arayos?
Seforno: With the promise that Hashem made to Avraham (in Lech-L'cha) to be "his G-d and the G-d of his children after him", 1 the Torah taught the Parshah of Arayos, so that the children should be worthy for His Great Name to fall on them. It therefore follows with the Parshah of Molech, to make it clear that, not only will sacrificing one's son in order to render one's other children worthy of serving Hashem not succeed, but it is also a Chilul Hashem.
Hence the Pasuk concludes "Ani Hashem" - implying that HAshem has not changed, and that that promise remains intact (Seforno).