Water pump pulley wobbling, belt about to jump out.

With the engine off, I notice that the pulley is not "flat" against the engine, but one side is clearly farther away from it than the other side. In other words, the pulley is sitting on its axle on an angle. When it runs, it wobbles and the belt is walking up the side of the pulley and about to come off; in fact, I think the only thing holding it in place is the presence of the second serpentine belt, which it rubs against and smokes.

The car is not safe to drive in this condition, and I am concerned that there may already be hidden damage.

What is the probability that the pulley wheel itself is the problem, and that replacing just the pulley wheel will solve it? If the pulley wheel is integrated with the water pump and cannot be removed, what is the procedure for replacing the water pump, what other problems should I look for as I do so, and am I crazy for undertaking this project on my own?