There is no hard limits between online and offline. Any world can be played either way, and the mechanics stay the same.

Game works completely offline no problem (as long as you disable cloud saves).
As for fun, definitely YES but its a different experiance. Game was made for co-op, and its most fun that way. Solo is kind of a solitary zen experiance. Its a little harder but far from unplayable. There is no story, almost no-one to interact with, but its a fun challenge.