Why is the normal force applied from the corner? How can I find the application point of the normal force?
The normal force will be distributed on the base of the solid in a way that it balances all other forces acting in the solid - just the same way that the normal force in any solid at rest balances all the other acting force. By equilibrium in the vertical direction, the magnitude of the normal force equals the weight. Then, with changing angular velocity, the normal force magnitude doesn't change but only its point of application changes - it moves outward as the angular speed increases. However, there is a limit on how far can it move outward: it can move at most to the end of the base, because it's application point must lie in the base.
Then, if the disc is spinning fast enough to be just to topple the solid, the force will be acting in the furthest point in can, as it is shown in the graphic.