The gearbox is probably a result of the clutch being on its way out...........if the reverse gears are spinning they will always crunch as they don't have a synchro mesh, and jumping out of gear is usually a damaged synchro mesh, which is commonly caused by crunching gears.

Fair enough on the alternator then i assumed it wasn't working, make sure the belt isn't too tight that will knacker the bearings. Should be a better car when youve given it the TLC then