Honestly not sure what happened in the first vid. I'm suspected too short of a distance and she bumped the fence. The second vid, the rider came back into the saddle much to early and cause your horse to pull a rail behind. If you freeze the last vid, at the same spot in the jump she is still off of her back just a little.
It's hard to critique the horse because the only shot is of the jump. Much of a jump is the set up way out before the jump and how the horse comes off the jump and prepares for what's next. From the short clips your horse looks good, could maybe use some more impulsion, but that's hard to judge. In each vid her knees are not level and some pointing down. You can use a bounce grid to teach her to snap them up.
As for your friend, I think she is grabbing with her knees and pointing her toes down. She isn't jumping ahead which is good but she does have the common habit of ducking. 2'1" does not require a huge effort on the rider's part. She needs to learn to let the jump just close the angle of her hip, not chase the jump.
All and all it's not a bad picture.
If your horse says no, you either asked the wrong question or asked the question wrong
And God took a handful of southerly wind, blew His breath over it and created the horse