Conceptual rolling If you could roll a ball down a slope with friction, we would all know which direction the ball is rolling. However, say we have a frictionless slope and we roll the ball in the opposite direction and place it on an incline. Would the ball roll down the slope rotating in the opposite direction? My intuition says that it would, because friction is the force that causes rotation, but it doesn't seem to make sense that a ball could roll the wrong way down a slope .
 A: Your intuition is correct. For the ball to change its angular momentum (to go from "backspin" to "forward spin"), there needs to be a net torque acting. There are two forces on the ball: gravity, and the normal force of the slope. Both these forces act through the center of mass - so neither force adds torque.

Without torque, there is no change in angular momentum. So absent any slip, the ball continues with its reverse spin.
A: The direction of the motion at any time $t$ is the direction of the velocity vector $\textbf{v}(t)$ as derived by solving the equations of motion; likewise $\omega(t)$ gives you back the direction of rotation according to the right hand rule.

friction is the force that causes rotation

is not entirely correct. Any force with non-zero torque generates rotation according to $\textbf{T}=\dot{\textbf{L}}$ and in the case at hand gravity may do according to the axes of inertia and other symmetries. I do not fully understand your scenario but anyway you should solve together
$$
\textbf{F}=\dot{\textbf{p}},\qquad \textbf{T}=\dot{\textbf{L}}
$$
to derive $\textbf{v}(t)$ and $\omega(t)$ and this will give you the answer.
