One: I don't see any attempt at a solution- just integrate!
Two: Since there are no bounds to the surface it looks to me like the flux will be infinite. Weren't there any boundaries given?
Three: You have copied the problem incorrectly. "Oriented by unit normals" makes no sense. There are two unit normals at a point of any surface. The orientation is given by choosing one of them. Oriented by which unit normal?