For your hands, you need to remember that they should be following the horse's head at the walk and canter, and remaining still at the trot. At the walk and canter, your horse's head will naturally move up and down, or rather, the motion will be back and forth. So keeping a light feel on your horse's mouth and having elastic elbows, practice moving your hands with his movement.
You can practice your two point at this time as well. You can grab a small bit of mane to get a feel for the motion (without putting weight on his neck) if that makes you feel more secure. At the trot, keep in mind that your hands will stay in the same spot, but your arms will still be moving. When you post up and down, your hands will want to follow up and down, but by bending and straightening at the elbow, you will be able to keep your hands still, and should help prevent the head-throwing.
I had a few students that had a similar issue with sitting back and having a chair seat. I found that getting them to rotate their pelvis forward (or in simpler terms, pushing your bellybutton forward), as well as opening your hands a little wider than apart than you would normally hold them, that seems to automatically make them sit up and open their chest. As for the leg, you'll need to just practice holding your leg back underneath of you, and do a lot of two- point and no stirrup work to strengthen it.
I really suggest working only at the walk and trot with him until you feel you are both strong enough to work at the canter. If he is having trouble keep his head and neck still at the trot, especially through transitions, that could indicate strain from lack of muscle.