Does the potential inside a hollow conductor change and why?
Potential is created by charge. Inside there is no charge. As one thing Issac Newton discovered in his calculus, is that only things inside the radius where you are exploring matter on particle forces, charge, or gravatitational. All the charge/mass outside the radius of understanding cancels out so the net effect is zero on eletric force, potential, or graviatational force, or gravitational potential IF IT IS UNIFORMELY distributed. Calculus magic.
Example, we know the Moon pulls on the earth oceans to make tides..but if the moon were instead a circular ring, it would cause all the force to cancel out, and there would be NO tidal force. Same thing on the chargeed cylinder, the charges on the cylinder if uniformly distributed, show no net effect anywhere inside the cylinder..the cancel out