Rolling down a hill backwards sounds normal, and being able to push it backwards in gear but not forwards sounds normal, but that "normal" implies the sprag clutch in the centrifugal, for engine braking, should be working, so it's strange the engine braking isn't working because it sounds like it is when you can push it backwards but not forwards. If you put it in reverse you should be able to push it forwards but not backwards if the sprag is working.
The starter sprag must be locking up if the starter can turn the engine, and if it was jammed solid and not slipping once the engine started, then you'd know about that by now, the poor old starter motor would have been doing about six times the revs it was designed for, and it would have almost certainly have blown up.. haha.. or made some terrible noise/vibration/smell.