Are the Q capable of travelling to mirror universes, alternate universes and/or fluidic space?
You could probably make a reasonable argument that Q is creating and entering alternate universes when he does things like transport the cast of TNG into Robin Hood, so it might follow that he should be able to travel to other universes as well.
Also, Q can travel through time. If parallel universes branch at every possibility, and they all ARE happening, there doesn't seem to be any reason why he wouldn't be able to follow one path or another, given the nature of his power. It seems to follow that a being that can travel through time could at the very least enter an alternate universe merely by traveling to the moment of choice, changing the choice that was made, and then moving forward again.
That said, there is no canonical example of Q popping up in anything that the characters refer to as an alternate or a mirror universe. The idea of alternate universes sees relatively little exploration in Star Trek, though.
"Junior" Q mentions going to fluïdic space in the Voyager episode Q2. So I'd think fluidic space doesn't seem a problem for Q.