A coin rests on a tilted surface being spun in a circle, what force causes it to slide up? If a coin is placed on a slanted surface and the surface is rotated about some center located away from the coin, the coin will overcome friction and slide up the surface.  However, the force acting on it is centripetal force directed toward the center of the rotation.  If you decompose this into normal and parallel components, the parallel component points down the surface, not up.  So what force is responsible for it moving upward?
In the following, every real force has no component directed up the plane.

 A: Your hypothesis is correct. If you adopt a frame of reference which is rotating with the tilted surface, then there is a fictitious centrifugal force which is $F_a=mr\omega^2$ in your diagram. ($\omega$ is the angular velocity of rotation and $r$ is the radius of rotation.) This acts radially outwards and has a component up the plane. If this component exceeds the component of the weight of the coin down the plane (plus any friction force) then the coin moves up the plane.
In an inertial frame, centripetal force is not a force itself, it is the component of real forces which cause circular motion. 
As you are aware, the only real forces acting on the coin are gravity $W$ and the normal reaction $N$ anf friction $F$ from the tilted surface. The horizontal componenents of $N$ and $F$ provide the centripetal force $m r\omega^2$. If the vertical component of $N$ is greater than $W$ and the vertical component of $F$ then the coin will move vertically upwards. As it does so, it leaves contact with the surface and inertia causes it to move tangentially in a straight line. This motion has a radial component which carries the coin horizontally back to the inclined plane. So it is the combination of the normal force $N$ and inertia which carries the coin upwards and outwards along the plane.
A: Centripetal force would keep the coin from moving up. If, and only if, the coin is not moving up the surface, there is (apparently) a sufficient centripetal force to keep it in place. But there is no guarantee that such a force would exist. In the scenario you are describing, the friction between the coin and the surface is not sufficient to keep the coin in a circular trajectory - so it slides up.
In a rotating frame of reference, there is a "fictitious force" called the centrifugal force - this is a force that seems to act on an object, and it is needed to explain why you need to apply a centripetal force on the object to keep it from moving (in the rotating frame).
There is no guarantee, in general, that there will be a sufficient centripetal force. But the centrifugal force is always acting in a rotating frame of reference. And that's the force that, in your example, is pushing the coin up the slope.
