This is assuming that the Confederacy would actually have remained and functioned with a central government. I always looked at the Confederacy as a collective reaction to the standing federal government of the United States. I would think that most of the states would have split from the Confederacy in light of its victory for fear of once again being under the jurisdiction of yet another central government.
Very possible. IIRC, Alexander Stephens actually urged Georgia to secede from the Confederacy during the Civil War.