I raised Pygmy goats for over ten years, I hope I can be of some help to you!
1. How long do they live? Be prepared to own one for many years, if you get it as a kid; they can live well into their teens...
2. How big do pygmy goats get? 23 inches (well 23 5/8 to be exact, at the tallest. They are generally 35-70 lbs...they are very stout, or should be, but shouldn't be obese, they are a very muscular animal, and come in solid black, black, agouti, and caramel coloring, with little white allowable. They cannot be anything but one of those colors, so when you see a palomino and white Pygmy, or a buckskin colored one, black and tan, etc, it's probably a Nigerian. They should be slightly longer than they are tall...but then this is coming from someone who bred to breed standard. I have seen grade Pygmies very quite alot from the standard, including in height and color. It's just that they probably aren't purebred pygmies when they sway that far from the standard, and when there's no papers to prove they are purebred, you have to assume that they have other breeds in them.
3. Do they need their hooves trimmed? Yes, every 6-8 weeks, and it's really easy to learn how to do yourself.
4. Is it safe to put them with horses? Yes, I've always had goats and horses together. The main thing is that you want a good intro period, where you can watch them interact; some horses like to chase small animals, and you want to make sure that's not going to happen.
5. What kind of fencing is appropriate for them? You will need a woven wire fencing for them. And you want it good and tight, and to the ground; it's also a good idea to put a board near ground level, to keep them from pushing under, and predators like dogs, from digging in. I like to make sure there are boards in the middle of the fence as well, as they like to stand on the fence, and it ruins it if there isn't more holding it there.
6. Do they need any kind of dental care like horses do? Some do, it's always good to check them periodically
7. Do they need any special vet care besides vaccinations and check-ups and are there any illnesses that only affect goats? CAE is probably the most prevelant, so make sure you get them from a herd that's tested free of the illness. They also are susceptable (goats in general) to bloat, and making sure they have free access to Baking soda can help limit
As far as other special care; they should have an annual Clostridium C\D, and Tetanus vaccination. They also need to be wormed every 8 weeks (sometimes more often, sometimes less often; but I wouldn't sway more than 2 weeks on either side). Rotate wormers, and if you live in a 'wetter climate' make certain you worm with something like Valbazene or Ivomec Plus, to ensure they don't fall ill due to Liver Flukes; there is no way of testing for flukes, which is why you just have to worm for them. The only signs of flukes are sudden death, or an animal that loses weight really quickly, and stops eating.
8. What kind/quality of hay do they need? Can I feed them grass/alfalfa mix that I give my horses? Any good mixture type hay will be good for them.
9. How much grain do they eat every day (they make goat feed, right?)?
They usually don't need a whole lot of grain per day...say maybe 1\4 lb. I never grained mine much more than gave it as a 'treat' everyday...Pygmies are very easy keepers