get a rope halter, and if he nips you, SMACK his nose, don't just ush it away because if you just nicely push it away a lot of them take it as a game.
If he trys to walk all over you "pin your ears" (just make your body language mean "stay away from me,i am boss here!" (it might take a while to get good at this so he understands.) and if he ignores it, snap the rope halter on his nose, which is the same as a 'bite' the lead mare would give him if he did that. Don't accept ANY bad behaviour, he is a horse, but that doesnt mean he can't be perfectly behaved (except if he actually spooks/is scared of something, even we get scared sometimes,so do hroses ;) )
As for the arena spooking, ignore it, he's either doing it because he's a little spooked, or because he's got extra energy and/or doesnt want to work, an that usually gets him out of it. Once he figures out your the boss mare from the groundwork, he will probably trust your judgement more and not spook so much when you ask him to do something. That's just what I've found with horses.
Good luck! :)
If there are no horses in heaven... im not going.