Have you tried brushing him? He could be molting, Rex rabbits from what i read have a plush coat that needs brushing. So this could help with the grooming. 

I don’t think its a loneliness thing, plus bunnies have to bond to each other. That’s a whole process that requires neutering/spaying, a month or two of healing, then a few months of pre-bonding. Then you can get to introducing them face to face. 

My sense is that when they bite their cage, it means they want to come out or they want attention. You mean that he has the ability to leave his cage (door left open, etc.) but he stays inside and is biting the bars? How big is his cage?

I think it’d be hard to say how getting a companion would impact his behavior – but you probably already know that it takes a while, the bonding process.

They do groom a lot, do you know around how many hours a day he does this?