Q:

Does the top of a spherical ball having a forward velocity and reverse spin appear to be at rest? 

Suppose we have a spherical ball with radius $R$. We give it a velocity $v$ towards left and a clockwise spin (angular velocity) $w$. The $w$ is given in such a way that $v=Rw$ is satisfied.  In such a situation the net velocity at the top of the sphere comes out to be $v-Rw=0$. So, suppose we mark the top of the spherical with some symbol (say "X") do we see the symbol moving or does it seem to remain stationary on the top as the net velocity at the top is $0$ ?  

A:

The symbol moves.  Only when the symbol $X$ moves to the top of the ball does its velocity becomes zero (and the trajectory makes a cusp there), but it still has an acceleration.  You can visualize the trace of $X$ by imagining how the velocity changes at different angles.  In fact, it is just a circle rolling on the "ceiling", so the trace of $X$ is an upside down cycloid.