You can feed the new bunny plenty of hay and give him pellets. Is this a young bunny, under 6 months of age? If so, he can have alfalfa hay or alfalfa based pellets. It would also be fine for him to eat the timothy hay. Diet is not so much dependent on breeds of rabbits, but it goes more by the age of rabbits. You would want to hold off on the veggies and fruits unless the rabbit is 3 months old or older. When you do start him on veggies and greens, go very slowly. Just try one new veggie every few days or every week. You don’t want to overload his system with unfamiliar foods. That could cause GI problems.

Since he is 1 year old, you can start giving him some greens. Maybe romaine lettuce would be a good one to start with, if they have that where you live. Otherwise, you could try one of the veggies you currently give to your other rabbit. The amount of pellets that you give him should be based on his weight. I just looked up mini rex rabbits and it says that they weigh between 3.5 and 4.5 pounds, so they are small rabbits and should get between 1/8 cup and 1/4 cup of pellets a day. Of course, they need unlimited hay.

The sneezing could be due to allergies since you don’t see any nasal discharge, but it’s also possible that he has an upper respiratory problem. It’s too bad that the rabbit savvy vet is not available. If the sneezing continues, you may need to take him to any vet that is available. Any vet can listen to his lungs and check him over.

You didn’t say if your female is spayed or not, but if she isn’t, be sure that you don’t let the bunnies get together for even a second, or you might end up with a litter. If you plan to bond them, they will have to be spayed and neutered first, then you let a few weeks pass after surgery before attempting to bond them. You should keep the new bunny apart from your female anyway, since it’s possible that he could have some sort of a respiratory infection.