A. No because it is in fact possible to prove something does not exist if its existence leads to a contradiction. For example one can show that there does not exist a pair of integers (m,n) such that (m*m)/(n*n) = 2. If there was, there'd be an integer that is both even and odd. (In others word the square root of two is irrational.)
If one can show that it is logically impossible for an entity to be simultaneously omnipotent and omniscient, then God cannot exist. Martin's excellent book Atheism: a philosophical justification has many such arguments.