I'm not really sure when you would ask someone if they can fall asleep on their own. It sounds a bit creepy and I'd suggest you don't ask that of anyone. The second question is okay, though I'd suggest the question "Does it take you long to fall asleep", whilst not asking specifically about the swiftness of the person falling asleep, would come more naturally to an English speaker. The third doesn't really work.

你可以一个人睡着吗？