When asking to back, a trainer showed me some techniques. Have a whip, of course, for cueing. The force of your BEING must make him back. Make yourself large and forceful. Shout if you have to. wave your arms. He must back away from you because you are dominant. One step back is enough--praise!! Good pony!! Ask to back again and be dominant. One step is enough at a time--praise!! Once he understands what you are asking, he will respond to a simple "back" or even your movement toward him in a dominant manner. He is not respecting you.
He must learn to back straightly, and that is what your whip cue is for. The whip is to cue the front shoulder to "steer" him.
As for biting, I have a gelding that I've never been able to cure. He is very mouthy about everything. He does not bite meanly, but as a brat. We've done so much pinching/smacking/yelling that in some situations (such as at hoof cleaning time) I just look at him and say "don't even think of it", and he minds his manners. But it is almost as though he can't help himself. I think it is very important to cure this at a young age--my boy was a 5 year old stallion when I got him and already was doing it. I've had him 10 years.
Interestingly, when we go to nursing homes and schools, do parades and petting "zoos", he has never nipped anyone. Crowds of children around him, petting and stroking, and he has never nipped. Old folks handling him, he never has nipped.