How can I dream things that are impossible?
Dreams aren't logical. Your mind is in a relaxed state when you dream. Thoughts become super-imposed and intertwined with each other.

Ideas and imagination is never directly related to interpretation. When you say you imagined stairs, it's actually your idea of stairs. It has no correlation to the real world at all. Your idea of stairs or empty space by themselves have no information related to how objects can physically move from one place to another. Therefore when your mind is being lazy and not focusing, concepts like logical physical movement can be ignored entirely.

We still don't know much about dreams that isn't still speculated about. These are some pretty good places to check out; How Stuff Works - Dreams, Wikipeia - Theories,  The Scientific Study of Dreams