You seem to have a clutch problem or the engine is revving to high.
At idle it should not move or stall in gear, the pedal on the right is
the rear brake. When you push the shifter down it will disengage the clutch until you release it. There are great sites devoted to these bikes, google honda supercub. Check the engine/trans oil.
perform the clutch adjustment exactly as described online.
contact me if you cant find anything, I have several ct90s & cubs.