First of all,
BYC has a sister site, Backyard Herds, which has a rabbit sub-forum. You can find a lot of information there. But let's see if I can't help you with some of the questions you have posted.
A cat nail trimmer is a great idea, the small blades let you see what you are doing and make it less likely you will take off too much. Like most animals, rabbits' claws have a "quick" of live tissue running partway along the length, if you cut a nail too short, it hurts and will bleed. If your rabbit has white claws, you can easily see where the pink part is. Black claws are harder, though if you can look at them backlit with a bright light, you can usually see it. If in doubt, look for the point where the claw begins to curve and taper dramatically, and cut outside of that point.
With practice, you can do a rabbit's claws by yourself. I put the rabbit on its back in my lap, and use one hand to hold the foot/toe, and the other holds the clippers. If the rabbit is just too wiggly, get another person to hold the rabbit while you concentrate on the foot and the clippers. Rabbits are usually calmer when held on their backs; it makes it easier to see what you're doing, too.
The rabbit needs fresh water available at all times, of course. If your rabbit has a water bottle, check it by tapping on the ball at the end of the tube - your finger tip should get wet. Sometimes the balls in the tube will get hung up, and not let water through. If your rabbit isn't eating, check the water bottle first - he/she needs water to process food, so if there isn't any water available, they don't eat.
If you can buy the same brand of pellets the rabbit is currently eating, great. If not, you need to mix the brand you are currently feeding 50/50 with the new brand for about a week before going completely to the new feed. Rabbits are prone to digestive upsets, so you don't want to make any sudden changes to their feeding. A good rule of thumb when feeding is about 1 ounce of pellets per pound of normal body weight for an adult rabbit (notice I said "normal body weight," this obviously doesn't mean that an obese rabbit should have more food than a slim one!)
The rabbit should also have access to grass hay (NOT alfalfa). Some people insist on Timothy hay, I feed Bermuda; the most important part is the fiber, so I don't get excited about the species. Hay is cheapest by the bale, of course, but if you are feeding just one rabbit, it could go musty and moldy before the rabbit goes through the whole thing, and moldy feed isn't good for anything! Some people like to feed just a handful every day, others advocate free choice hay, the most important part to me is that it be clean and reasonably fresh. As I said, hay provides additional fiber in the diet, which is important to rabbits. Rabbit lick themselves like cats so they ingest hair when they do, but unlike cats, they can't vomit, so the hair must go out the other end. Hair can build up in the rabbit's stomach, causing a condition called "wool block," the fiber in the hay helps to prevent that from happening.
If you live in the US, the wild rabbits in your yard are not only a different species, they are a different genus as well. Your rabbit can't breed with them, but there are diseases and parasites that it can get from them, so it's a good idea to keep it well away from them.
This link may help you figure out what breed your rabbit is. If you click on a breed, it should take you to the breed club website, which will have a bit more about the breed itself:
http://arba.net/breeds.htm
The gender is a little trickier, but to some degree that will depend on the rabbit's age. A mature buck will be hard to miss! Flip the rabbit over. At the base of the tail, there is a little fuzzy bump. If the rabbit is a mature, intact male, the testicles are clearly visible, one on either side of the bump. A rabbit can draw the testicles back inside his body, but the slack skin will still be there (does have bare patches there, so don't be confused by that). If the rabbit is, say, less than 4 months old, you may need to get a bit more personal with it. Pressing on the front of the little fuzzy bump will expose the rabbit's genitalia. If what pops up is round, it's a male. If it's V-shaped, with a slit-like opening, that's a female.
Congrats on your new bun!
