If you had a glass ball filled with water, completely sealed and containing a fish, could the fish move the ball?
Yes, with gravity and a generous definition of "moving".. it would be the same principle as the toys where you can control a sphere using a radio control (or using your iphone). The fish swims along the edge and gravity pulls it back down, which starts a rotation of the water and by friction to the sphere starts the rolling motion of the sphere on the ground or other surface. Obviously the water/sphere friction will probably be miniscule, but at least it is possible in theory :)
A follow-up question would of course be if it's possible to move a hermetically sealed sphere freefloating in vacuum and without gravity or any other appreciable fields intersecting it. If you solve this, I'm pretty sure NASA will want to talk to you (or the fish)!
Yes, the fish could (theoretically at least) move the ball.
A quick way to visualize why this is so is to imagine yourself sealed in a 7-foot diameter ball of air. You could easily move the ball by walking in the direction you wanted it to go. Of course you would have a much easier time of it, since your density is much higher relative to the surrounding fluid (air). The fish's density is much closer to the surrounding fluid (water), so it would have a harder time of it.