Yes, the three are supposed to be related, and are collectively called "Abrahamic religions".
I read widely, and don't believe what I read unless it's supported by compatible evidence. I spotted that those who were not of one of the Abrahamic religions were to be enslaved, converted, or killed and investigated it as potential threat to me. This has been verified to my satisfaction.
Christians and Jews are supposed to be allowed the fourth choice of become Dhimmis by paying the Jizya, but I've read from several sources not related to one another exactly how Dhimmis are treated (thus the "good nigger" comparison).
One big thing to remember when listening to or reading something a Moslem is that what the words mean depends on who the Moslem is talking about.
If a Moslem tries to strike an unbeliever and the unbeliever blocks the blow, the unbeliever has just attacked the Moslem. We all know families like that. They try to thump you and you defend yourself, you have just attacked someone in that family. If one of them takes something from you, that is not theft. If you take it back, that is theft. And so on. That's the Islamic attitude toward outsiders.
By the way, Atheists are also to be killed, enslaved, or giving the conversion option. Saying you don't believe in any gods is regarded as an attack on Islam, punishable on the spot with death or a severe beating. Atheists have no legal protections and trying to bring charges in a Sharia country will result in death or enslavement.
If a Dhimmi tries to dodge a blow or blocks a blow, he has just "attacked" a Moslem, and forfeits all the "protection" he bought. A Dhimmi who discusses his religion has just "attacked Islam" and forfeits all protection. Of course, that "protection" was worth a word's weight in gold as Dhimmis can be beaten, robbed, killed, raped, etc in spite of what Islamic law says (recall the bit about unbelievers cannot testify in Sharia courts and how Moslems are prohibited from "befriending" unbelievers?).
Yes, from what I've read, early Islam was influenced by the Gnostics, and probably several other branches of Christianity that have since vanished, along with similar branches of Judaism. That's probably why Christians and Jews are given favored treatment, murderous oppression, instead of outright genocide.