I am out. Until you do the proper tests you will get nowhere. The key way gap is fine a little experience would tell you that. The ops experience is not who I question.
Actually no. The shifter has a washer on the shift rod that pulls the fork up in forward only. If the cam pulled out of the lower the motor will be unlocked on reverse and neutral.
You need to be at a certain Rpm in gear and idling. I think around 750 rpm is right for that motor. There might also be mix screws on the carb that need to be opened a little bit. Get a manual for your motor.