1) Can you capture cave dragons with cage traps?
Yes, they don't have TRAPIMMUNE.
2) Is there a limited population of cave dragons, like there are above-ground-dragons?
There's a limited population, but not in the same way as regular dragons. Regular dragons are unique creatures which are created when the world is generated, and seem to never or very, very rarely reproduce during world history. Cave dragons are treated like any other wild animal - there's a fixed population generated for each biome they exist in, and once you kill or capture all those there aren't any more. Dragons, being megabeasts, can travel from anywhere in the world to visit your fortress. Cave dragons will only show up if there happen to be some in your local cave biomes.
3) If you have a tame female cave dragon and a male cave dragon, can they breed?
Not without modding. They're [PET_EXOTIC], so they won't breed in unmodded DF. They have no CHILD tag either, so even if you mod them to be [PET] they can't make children.
edit: 4) The wiki says the cave dragon is only found in -dry- evil caverns. How do I determine if a cavern is evil or dry?
They are found in [BIOME:SUBTERRANEAN_CHASM], which means the caverns that have land as opposed to those which are flooded with water.
I'm not sure yet what [GOOD] and [EVIL] mean in relation to caverns. I've caught gorlaks, which have [GOOD], in caverns under non-good surface biomes, so it's not related to the alignment of the surface biomes. There might be an invisible good/neutral/evil status on cavern biomes that you can't see when embarking. I've also heard that it has to do with the depth of the cavern, with the lowermost layer of the caverns being [EVIL], but I don't know if that's true.
Note that cave dragons have [FREQUENCY:5], which means that only 5% of embark sites with the right biomes will even have them at all. They also have [POPULATION_NUMBER:2:5], so there's only 2-5 of them in an embark site if there are any at all, and they have [UNDERGROUND_DEPTH:3:3] which means you'll only find them in the lowest cavern layer.