Problem: Your backhand is a critical deterrence in your game. It's preparation is a little short, and weak so you can't produce a strong one-handed backhand. In addition to that, you follow through more outwards than you do upwards for topspin which is what's causing your backhand to constantly go into the net.
The Fix: Practice swinging normally with the correct technique of a flat backhand UNTIL your contact point which should be out and in front of you. After you stop at contact, practice swinging upwards. Then, when you do this quickly your racket's contact will be a little higher but able to produce more topspin. For low balls you'll have to bend your knees a lot more. You'll see a lot of the Pro's doing this. I recommend watching Henin. She hits everything with a one-handed backhand except running shots which are usually sliced.
Also, what's up with your forehand? Is it a Western grip? Western grip gives nothing but topspin for the purpose of net clearance so when you swing the racket should be flat from contact all the way to the follow through, but in your case it seems to be opened up which causes the ball to lob a lot.
Also at 4:00 there's another watermark.
Your friend also forehand slices everything so...tell him to make some decent/better hits. Forehand slices except when running for the ball makes me sad.