Well, b seems rather straightforward, just plug it in.
For c, you could show that there is a point for which the limit value depends on the path you take. For example, showing that
[tex]\lim_{x \to 0} F(x, 0) \neq \lim_{y \to 0} F(0, y)[/tex]
would prove that F is not continuous at (0, 0) because then it shouldn't matter how you get to (0, 0). I think that b should give you a hint on which point and paths to consider :)
