A883 2nd & 3rd question

Yes it could. Could be other stuff too. Like; shifter/linkage alignment/loose levers/worn combs/bad back bearing/driveline vibration/engine shake/tranny mount.
But the most likely thing for a no load pop-out is insufficient engagement, due to a very worn fork. The steel forks can easily be repaired(hard brass brazing). The cover can be removed from inside the tunnel.

Jimmy, before you pull the cover, check the other stuff, especially loose external levers on their mounting studs. They HAVE to be tight. I think the cover comes off easiest if in 2nd? Its pretty tight in the tunnel. Have fun putting the gasket in there! lol.