This is really a great video, breaking down the mechanics as well as why this shot is so important. Have you tried the TopSpin Pro? It might be a good addition to your teaching -- spot on to everything you are saying...
Topspin is great for pickleball, obviously. That's why tennis players easily dominate. However, you mention that topspin is integral for any racket/racquet sport. That's not true. You would never hit topspin in racquetball. I don't play squash, but I'd imagine you wouldn't use it in that sport either.
Don't mean to be ticky-tack but the proper term would be swinging from "below" the ball not "under" the ball. "Under" could make some people think you're trying to contact the ball below the equator or the underside of the ball. :) Liked your tips about the footwork/closed vs. open stance. Thank you!
Swing waist but keep back leg 'anchored' as you finish swing with paddle up over shoulder. Lifting back leg as you turn is ok, just don't loose it finishing shot.
It depends on the type of shot. I do snap my wrist a little on the drive, but that comes from years of playing tennis and badminton. On drops and dinks, I keep that wrist stable to give myself better control.
You’re not hitting the ball like you are describing you are hitting the ball. You cannot contact the ball with a closed face. Otherwise, you will contact the ball above its equator and it will go straight down. I think you need to emphasize that as you brush up on the ball, you need to hit as you’re facing the ball under the equator of the ball and coming up otherwise if that ball was not being lifted it is going to go into the net