That's very usual. I know sometimes rabbits can hit things with their nose to move it out of the way. If he is banging his nose against it, maybe there is an issue with something irritating his face or gums. If the skin breaks, then he could cut his nose and it will be harder to stop him. He might want to be let out of his cage. Rabbits need space and when they want to be let out they can to random things to get attention. Being in a cage all day is very boring. Also make sure he has things in his cage to keep him entertained.
If he has an itchy butt then he could have faeces stuck on his tail and this is annoying him. If so you need to clean it with a warm soft wet cloth with pet wash. This happened to my guy before. Wear gloves.
Try changing his daily habits to see if anything stops him. Also try putting in a bowl of water and take out the bottle. Some rabbits prefer the bowl over the bottle.