Timothy hay is the best choice for rabbits, but please also add fresh green leafy vegetables to his/her diet.
Alfalfa hay can sometimes have too much calcium and cause urine issues. The urine you describe is normal, because rabbits pass a very concentrated urine that is high in calcium. Because of the high solute composition of their urine, rabbits can get urinary tract infections.
Males have testicles, unless they have been neutered. They are elongated tubular structures that lie along the sides of the hind-end of the belly. You may not be able to see or feel the testicles because male rabbit's can pull the testicles up into the body cavity. They have a penis that appears as a small rounded mound in the mid-hind-end of the belly. Males don't have nipples either! A vet can let you know if you have difficulty in determining the sex of your bunny.
Bunnies can live to be about 8 years old, or so.
Your new pet should be checked out by a vet. Rabbits can get ear mites, ear infections, ectoparasites (fleas, ticks, mites), and internal parasites, especially if they have been living outside. Rabbits are especially susceptible to bots. Bots are larvae from flies that become embedded under the skin, after flies lay eggs on the skin. The fly larvae lives this stage of it's life cycle under the skin of the rabbit until it is ready to change (metamorphose) into a fly. It can cause a skin infection on your rabbit that may require antibiotics. If you plan on leaving your rabbit outside in a hutch, please make sure that the screening is fly proof to avoid a bot infestation.
The most important disease that rabbits can transmit to people are parasites and ringworm, so it is important to have the stool checked, and an examination of your rabbit's skin and hair coat by a vet. Other zoonotic disease are very uncommon.
Good luck with your new pet!
While you are waiting for Dr. Cheng to answer, I would suggest a visit to the vet to be sure all is in order with the bunny's health, and to find out the sex if you are not sure. I believe the vet could also test the bunny for parasites.
Hopefully Dr. Cheng will have more helpful info, but personally, any animal that I would find, I'd take to the vet straight away for an exam.