So I see a lot of tension in her riding - her back is arched, her knees appear to be gripping (causing her to bounce on saddle), and she's "pumping" at the canter.
I'd have her take some "lunge line" lessons - sans stirrups - to get her confidence back.
1.) Start with working the walk (not really shown on video). Have her remove BOTH legs from stirrup leathers and take her legs OFF the saddle. Can she stay balanced with her legs not touching the saddle? If not have her totally relax her body and grip front of saddle to stay on (lunge line handler controls horse). Next allow her legs to hang down nice and long from the saddle totally relaxed. Don't worry about heels down. Many time when a rider forces their heels down it causes them to stiffen their legs and causes tension in their riding.
2.) Once walk is good add the trot. Start with sitting trot, no stirrups. Again idea is long legs NOT gripping but relaxed abd no bouncing on the saddle. Grab front of saddle as needed. Once she can sit and stay on without bouncing or gripping wioth her legs then have her do rising trot. Still without stirrups. Be sure to tell her to place her elbows ON her waist and as she rises with the trot to "open" her elbows, as she sits to "close" her elbows. That keeps a nice steady contact with the horses mouth, another problem of hers. Once she can so sitting and rising trot without fripping or moving her armws up/down as she rises she can get her stirrups back.
3.) Canter. She is "pumping" her body at the canter. Instead she needs to relax (there's a theme here
) and instead of "pumping/pushing" with her seat instead think of lifting her ribcage as the horses mane rises up into the air.
Overall tension is causing most of her issues. A good dressage instructor could help her as could a jumping instructor who knows basic dressage techniques. She should stop jumping altogether until she can ride again - because the jumping issues (leaning forward about 4 strides out, falling on horses forehand after jumping, etc.) are most likely tension resulting from a lack of confidence.
The small jumps she's jumping in the video should not cause her butt to leave the saddle - instead have her just bend forward from the waist and NOT ride out of the saddle for these - then move hands forward towards middle of the neck (NOT a crest release - that's for beginners). I believe she needs to re-start herself on the basics of riding to re-establish her confidence before jumping. Something has scared her and this has resulted in tension which has changed her from a competent rider into one with issues.