Wadda ya want?! The cold, hard, facts of Angelology? How many baalim can dance on the head of a pin? Beelzebub’s shoe size? 
The OP question (boiled down a bit) was: “Could you please help me trace the etymology [of Beelzebub] from Kings I to being another name for Satan?”
As CKDextHavn and cmkeller have noted, the etymology of the name is well understood.
The path from baalim to demon doesn’t appear all that mysterious either, the same transformation has been applied to any number of other deities, Semitic or otherwise.
I will have to leave it to wiser minds to explain the socio-theological reasons for the shift from “our god and their gods” in the Old Testament, to “our one **true **god, and their evil-false-can’t-be-gods-so-must-be-demons” of the New Testament.
As for why Beelzebub (rather than Belphegor, or whoever) gets to be another name for Satan, check the Davidson quote: *
Beelzebub is chief of the demons, “prince of the devils” (as in Matthew 12:24), but he is to be distinguished from Satan (just as he is in all magic, medieval or otherwise). *
Looks like Dante did consider him the same, but other writers have not.
On a more serious note… what more information do you require… you said that it was related to a class on Thursday. What other info would help? Would it help to know why Beelzebub was considered a “prince” among demons, or why Dante considered them the same, or…
We will ferret out the SD… Baalcecil or no. 
PS: I’ve often thought that I’d like to name a cat Beelzebubbles.