1. Actually ordinary dragons should be able for a some time move through water. So underwater battles are possible in theory. Question is will those be scripted well enough to make it possible.
2. As far as I remember elemental dragons are from D&D lore, in TES all dragons breathe fire, they simply can be of various types (red&black for example)
Lore concerning TES dragons is vague, but it's been suggested that fire is just a by-product of the dragons speaking, and so is a lot of other funky stuff. Hence the whole "Dragon Shouts" theme we've got going.