Why charge is zero inside a conductor
The electrostatic field is zero AFTER equilibrium is established (after the internal E-field cancels the external E-field.)

Remember the equation that describes the introduction of charges at some interior point of a given material:



What it means is that any charge introduced at the interior of the conductor will decay immediately and appear on the the surface.

Stated in other way, if some charges are introduced in the interior of a conductor, the charges will move to the surface and redistribute themselves quickly in such a manner that the field inside the conductor vanishes.