If he's a school pony, then it will be more difficult to keep his handling consistent, which is the most important thing for keeping expectations of him very clear and maximizing the effectiveness of any training. Firstly, if he's not your horse (I'm assuming this is the situation, based on the OP), get permission from the owner before doing anything with him, period. Respect their response. If he's your lesson mount, ask your riding instructor if it's ok to do anything about the behavior, and/or for assistance in dealing with his behavior. From here on, I'll answer under the assumption that you are not the pony's owner, but do have permission to handle him.
Nipping and biting can be tricky to fix, and the best method to tackle the problem varies from horse to horse to some degree. In general, though, I would say refrain from feeding him anything by hand, and don't keep treats in your pockets to tempt him into testing boundaries. Alongside this restriction, keep yourself aware of what he's doing with his mouth - if he goes to bite, pop him on the shoulder and drive him out of your space quickly. You're trying to get his attention, so make the response to the attempted bite big. Let him know that biting means that you're going to make him work.
As far as him being pushy with his head, I see that as a different facet of the biting - he's just not respectful of you. I recommend doing the same as for the biting. If you're in the habit of allowing him to scratch his head on your shoulder, don't let him: people aren't scratching posts. If he gets pushy, reestablish your personal space and move his feet away from you. If he tries to barge past you, back him up. Don't accept little halfhearted responses - he needs to respond to your requests promptly and snap to it with a real "yes ma'am/sir" attitude.
All of this will help him to trust you, as he begins to see that your responses are sensible, reliable, and make sense from a horse's thought process. You're establishing yourself as a dominant horse in his herd, an alpha worthy of respect and trust.