He sounds like a pretty confident horse! For the rubbing, the easiest way to deal with that is to not let him in your space in the first place. You go to him if you want to pet him. If he does start to rub on you, use your nails and scratch him HARD on his face, hard enough to be uncomfortable to the point where he backs off. Whatever you do, don't move your feet. The one who moves his feet first loses the 'game.'
For the grooming, make sure you aren't accidently pulling on the lead rope, and make sure your energy is down and that your body language isn't telling him to move. If he does start to move, just rub him to a stop and start again.