Unfortunately, the best course of action is to go to a vet and get an xray done and formal assessments. There are a lot of things that can cause what you’re describing, and all appropriate interventions, like surgery or medication, can only be obtained through a vet. Can you send videos to the vet for some guidance?
Him trying not to move too much means he’s probably continually hunching, which is a sign of pain in rabbits.
Is your rabbit neutered, and is his brother neutered? Also, how long have they been together, before you separated them? If they are not neutered and you have separated them from each other because of what’s happening with the rabbit who’s injured, it could be his brother attacked him and hurt him, because they are not bonded. Rabbits do not have family units. Brothers are the same thing as strangers. They get along when they’re babies because they’re babies.
The emphasis is though, you need to see a rabbit-experienced vet.
For the missing nail, have you ever clipped his nails before? Losing a nail, one of the main causes, is the nail is too long so it snags on and gets ripped off by something.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.