So did he rape her while she was unconscious?

It is a long time since I saw this film but from memory he had some weird kind of a 1930s Hollywood idea that nice girls did not have sex. Even when she tried to seduce him so she could get away he would not be in it, so no.

I am not an expert, and if you mean rape as in intercourse, I think she'd have some idea if he had regardless of what he says. Without much by way of consent there is just too much force necessary and leaves some damage.

Some people are afraid of the unknown. I don't know why, and it scares me.

Possibly, but he was impotent, so it's ambiguous. He liked dead things as Miranda pointed out and perhaps could get aroused if she seemed tto be dead.

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I personally don't think he did, but I can definitely see potential for ambiguity. He does "lose control" in that early scene outside where he's caressing her face, suggesting that had she not screamed and brought him back to his senses he might have been capable of actually assaulting her regardless of his convictions about extra-marital sex being morally wrong. And he's lied to Miranda in earlier scenes, so you can't entirely take him at his word.

Of course, in the novel I believe the character was impotent, but I don't think they suggest that in the film... though I've only seen it once.