Fishbowl.

You fill a round goldfish bowl up with water, drop the fish in, and then seal the top to make a perfect glass sphere.  Assuming a level plane, no air bubbles in the water, minimal friction with the ground, and sufficient amount of oxygen dissolved in the water:

Can the fish make the bowl go forward?

I would imagine so, in the same way that a hamster can walk in a hamster ball. It would require a very strong goldfish, though. What I imagine it doing is swimming in a circle until the water inside the sphere develops a current. This motion is then transmitted to the bowl via friction, causing it to move.

That is a good question. I would say that the fish could move the sphere forward by hitting the it's wall, but by simply swimming I would say hardly. If anything, the bowl would move backwards in my opinion since the fish is moving water molecules behind itself which will exert a pressure in the opposite direction of the movement of the fish. It really depends on the form of movement (I somehow thought about a human swimming :/) though.

If they fish is more dense or less dense than water it can.

The fish cannot force the bowl forwards by purely translational means (Newton's 2nd law).  Using the hamster wheel analogy, it can make the bowl spin (maybe?).  For the spinning bowl to move forwards though, requires friction with the ground, which is stated to be negligible.  Hence the bowl stays where it is ad infinitum.

Yeah >>5 is right. If there is no friction, the force applied for the bowl to move would have to be outside of the system.

No.?