Does NADH provide energy to move protons out of the membrane or does it send its own proton out of the membrane? When it oxidizes it produces a H+ so does this have any significance. I mean can any reaction that produce energy move the protons out of the membrane. Thanks!!

It does nothing on its own. It essentially only provides the input into the electron transport chain. The transfer of electrons from one complex to the other within the membrane is then coupled with the transport of protons out of the cell, which builds the necessary proton gradient for the ATP synthetase.

NADH is an electron acceptor. Meaning that it carries the electrons to the ETC. Once there, it deposits the two electrons. The movements of the electron through the plasma membrane and the complexes embedded between allows the protons in the Mitochondrial matrix to move up their concentration gradient and into the inter membrane. It is the electrons that supply the energy to the protons. NADH is only the electron carrier molecule.