Suppose we had a hollow conducting sphere with a net charge q on it. There is no charge in the cavity; the conductor itself has a charge q. The idea is that this net charge would reside on the 'surface', since the conductor has free charges otherwise to make the net field inside the meat of the conductor zero.
My question is with regard to what 'surface' means. Does 'surface' refer to the interface between the conductor and air? If so, why isn't there charge residing on the inner surface of the hollow sphere? Has this something to do with uniqueness theorems?
Related question: If there is an external charge q outside an uncharged hollow conductor, why is there no induced charge on the inner 'surface'?
Also related: How is it that information of charge inside a cavity is known outside, but that outside is completely unknown inside? In a sense, aren't both regions of air the same and separated by the conductor only? Better put: when there is a charge inside the cavity, the inner surface charge distribution cancels the field in the conductor due to the cavity charge, and residual charge q sits uniformly on the outer surface, thus 'revealing' the presence of q to the outside. Why does the same not happen to a charge outside?