Answer to POW #1:

It is not possible. Because of the way that the knight piece must move, after every move the color of the square that the knight is on switches. Therefore after an odd number of moves, the knight must be on a black square. The path described would consist of 63 moves, so it could not possibly end on the white square in the top left hand corner.

Source: Len Van Wyk told me about this problem.