Young horses need to be given clear instrucitons and have their behaviour boundaries clearly defined.  When he pushes you apply gentle pressure to his nose with one hand and using two fingers push him in the chest to make him back up.  Never let him rub his head on you.  You are not his rubbing post and this is only tolerated by submissive horses.  If he steps on you make your response the same - make him back up.  Be stern, make your body language strong.  Let him know you will not tolerate this behaviour.  You don't need to be harsh but your response must always be fast and consistent.  With regards to the biting, this is one thing that must be stopped straight away.  I find that a sharp rap on the lower jaw with the back of the fingers is very effective.  He can't see it coming but it must be done as he threatens to bite or at latest when he is making contact with his teeth.  Never hit him around the head.  And last but not least we often find that putting a dominant young horse in with  group of older horses does wonders for his manners.  Nobody trains a young horse better than an old one.