Intuition behind Relativization
You haven't really asked any question, but it seems like you don't know what $\rm{P}^A$ means and what $\rm{NP}^A$ means for a language $A$.  The class $\rm{NP}^A$ is simply all languages that are decidable in "NP time", given a turing machine with $A$ as an oracle.  This means a non-deterministic turing machine with access to $A$ which runs in polynomial time.  The $\rm{P}^A$ is the deterministic version.