I really like that you video everything. It is alot of fun to watch. I also really appreciate to hear what the coaches say. It is fun to learn new things
Is it only private coaching in korea?
I think it looks good, you do not miss much! And you should proably listen to your coach but i have some thoughts that you can listen to if you want and try them if you want
I think you should have the elbow a little more in front of the body and have it steady, and accelerate with forearm and wrist around the elbow. In my opinion you should not move the elbow much in the backhand, but more use it as a steady point from where you move the forearm and wrist from. Like the hinge when you move and close the door. Feel that i have trouble explaining this with my limited english. Hope you understand
I also think you can try to close the angle of the racket. If you do this you will come more over the ball and get more spin on the ball. It sounds and looks like the hit is pretty thick.
Good luck and keep posting videos