You are going to see a lot more about Jesus as you go forward. Muhammad was evidently shocked and horrified by the idea that God could have a flesh-and-blood son and viewed that as idolatrous, but was also very impressed with Jesus as a prophet. Muhammad also will maintain that Jesus didn't actually die on the cross, but rather, a body double of some sort was crucified in his place.
I've heard (to be verified, I'll look for the source) that some early Christians apparently believed that and believed that Simon the Cyrene was crucified in his place, so that may be where the idea in Islam was inspired from.
Yes, this is correct. In book 1, chapter 19 of the five-volume work
Against the Heresies, the second-century Christian apologist Irrenaeus of Lyon cites and criticises the views of some early Docetists that, when he took Jesus' cross, Simon of Cyrene was transfigured by Jesus to look like him, and while Simon died on the cross, Jesus looked on and laughed at how he had tricked everyone. Irenaeus, however, attributed this view to an Egyptian Gnostic, Basillides, while later apologists such as Clement rejected that attribution. The second-century Gonstic Apocalypse of Peter also claims that a substitute took Jesus' place on the cross, but does not name the substitute. So, whether it was Simon of Cyrene or someone else, the view that Jesus' place on the cross was taken by someone else seems to have been fairly widespread among Gonstics and early Docetists. I think Muslim Qur'an scholars tend to the view that Jesus selected one of his young disciples to take his place on the cross, and not a bystander or stranger.
In any case, yes, please continue with this helpful and fascinating discussion.