1) Knees bent, slightly flexed (as has been mentioned) for cushioned movement, and I try to mix a "shuffling-drag" with a "rolling foot" movement (depending on the direction I'm going, the terrain, etc.) In short, I want to "feel" a curb, pothole, rock, whatever, before I try to put weight on it.
2) I see the point you're making about draw, then move, however, (for me) if I am doing that, it's likely to be at contact distance, and I'd be making a retention shot, then getting the heck out of dodge -- That is to say that if I "Stand and draw" I'm going to fire the first shot standing, then begin moving backwards. Again, it's all about the hits on target, and stopping the threat. One way to stop a threat is to be far enough away from it that it's no longer an imminent threat, and another way is to take the fight out of it. This technique combines both.
3) Spend some time with a water bottle. Fill it about 1/2 full, and hold it at arms length in a shooting grip. Now start moving. See how much the water is bouncing around? Your sight/muzzle are doing the same thing when you're shooting on the move. By moving around with the water bottle, you can learn to control this effect somewhat, and find out what works for you without firing hundreds of rounds. The water bottle is neat, clean, and makes no mess -- the first time someone mentioned this technique to me, it was described as a "hot cup of coffee over your wife's white rug."
Of course, the technique works either way, because you get direct visual feedback, and practice is key to shooting on the move.4) I second the suggestions above to shoot with some of the action pistol groups (IDPA/USPSA, etc.) because they do a good bit of shooting on the move. Granted not as much as we used to in IDPA (new rules and such), but it's a great exposure to the techniques, and you get to watch several other people doing it too, and get tips, hints, and an opportunity to see what works and what doesn't.
And most importantly, don't beat yourself up over it. Shooting on the move is probably the single most difficult handgun skill to master. It combines all the fine motor skills of shooting a handgun well, with all the fine motor skills of walking well -- most of which we take for granted individually, but stack up to make it difficult! It looks like you're doing pretty well, and that you want to improve is the single most important factor to success.