I’m kinda new with bunnies and bunny care, but here are my two cents..
First, how big is the cage? Maybe the cage contributes to why he feels territorial. Have you considered an exercise pen or a bigger enclosure for him? Maybe he will get used to running around then, and you can slowly give him more freedom and more space to play in. You have to give a rabbit time to trust you. Maybe once you get the larger enclosure, sit in his room for a while (read or do something that takes some time), but don’t encroach his space in the enclosure. Just wait for him to become curious and eventually come out to you. Or you can lure him out with a treat or fresh greens to speed up the process. I would resist the urge to physically carry him out or handle him because this will probably just make him even more nervous around you.
As far as the water goes, my Dorothy is very comfortable here and drinks water regularly, but she’s just naturally a messy bun and will sometimes step in her water bowl or her loose fur will end up in there. There’s hay in there often. The water bowl is often dirty and we change it out often, but she drinks it dirty or not. So I’m sure the fact that there is fur in there won’t deter most bunnies from drinking. He may be stressed. And from what I have heard, it is best to not bond older rabbits with younger rabbits in the event that one outlives the other it complicates things.