Lots of interesting stuff here. Shooting while moving is actually not that hard and doesn't require any super special techniques. It's all about keeping the front sight on the target and trigger control. Which also means practice, practice, practice. You should be practicing from a VERY close distance and moving away from the target at varying angles. This is much more realistic. I can't think of a scenario in which you would be advancing and firing from 25 yards in self defense. Advancing drills would be 5 or 10 yards max. You can also dry fire practice these all day long. Just watch what the front sight is doing when you "fire", that's were the bullets go.
Moving while shooting is a good thing if you're not behind solid cover(you want to be the hardest thing to hit), and the BG is not moving. Trying to hit a moving target while your moving is one the hardest shots there are. Best to pause and shoot, but only if the BG is moving also and you have enough distance.