If there is no light fixture on the ceiling is it possible to install a ceiling fan? Can power be run to the ceiling fan mount?

The quick answer is 'yes' and 'yes'. Anything is possible.

The real question is "how difficult will it be?" It'll be easy if you can get access to the ceiling (such as if there is an attic above). Not so easy of both ceiling the floor above are finished.

Yes. You can run wires through the ceiling, through the attic, on the surface of the ceiling via wiremold, or use a swag kit.