I frequently use "can't have", but it depends upon the context and the meaning I'm trying to imply. As Frank has said, yes it is correct. Also as Gary has said, in this context, "can't" has a stronger feeling or tends to negate or imply the improbability of whatever is being disputed. "She can't have gone to bed. It's only ten o'clock" implies that the speaker disbelieves that said person has gone to bed which further implies that said person probably stays up rather late and this going to bed at 10 is out of the norm. This could easily be what my friends say of me as I too tend to stay up late provided that I don't have to work the next morning. Another context as an example would be, "He can't have eaten all of that candy by himself." Again, disbelief here that the candy was eaten by one person. Highly doubtful. or "She couldn't have washed those dishes in only one hour." - disbelief that the event occurred. I think the difference might be likened to disbelief vs doubt (can't vs couldn't have respectfully).

Yes, I think you're right. "can't" is stronger, and suggests that it's impossible. That could be a joking reference to the fact that she's normally up late, or it could also mean that there's some practical reason that she would not have gone already. Both are fine - I don't know what Frank is referring to with regard to "can't" being strange, apart from possibly the slightly odd context that it is being used in.

No difference. The "can't" for a phrase like that would not be used in American English.