Central to the spin behaviour is the relationship between roll and pitch moments of inertia. Most light aircraft will have a stable balance. If you then check out the control matrix you can see the relationship between the rates of roll and pitch, which should explain why roll and yaw can cause the pitch oscillations.
Is it mostly the case that when light aircraft enter a fully developed spin it is "buried", ie both wings are actually stalled but the inner one more than the outer. The pitching moment effects of this with the stick fully back can cause the old "nodding dog" effect as the nose tracks around the horizon, the same as it would in a straight and level stall.