If she's already in the cabinet, does she have to go through that again?
NSA aren't confirmed by the Senate, so I think she still needs to go through the process.
Of course.
Any person, even if it is a re-confirmation, need approval from the Senate.
She is not in the cabinet. White House staff, of which the NSA is a member, do not have to be confirmed by the senate. However, to answer your question more directly, if a cabinet secretary switches from the head of one agency to another (e.g., Secretary of HUD to, say, Secretary of the Interior), that person has to be reconfirmed. New job, new confirmation hearings.
she's not officially a cabinet member as NSA.