Bats fly over water because they're the size of rats and mice. Hippogriffs are usually described as being the size of horses and would presumably have a wing span that much bigger too. No way they'd be able to flap their wings in such tight confines.

Question is, what are they doing in tight little caverns anyway?

Better question, how do titans and giants fit in these "tight little caverns?" I think if the space is large enough for these creatures to fit, hippogriffs should be able to fly.

The caverns are big enough for a titan to stroll down yet narrow enough for your path to be blocked by a rat.

If they're gunna fly, it's only fair griffins do too. And bees. What about vortices? They're just wind anyway, any reason they couldn't cross a body of water?

They're not bees, they're giant bees. They may have wings, but they wouldn't be able to provide enough lift to really fly with confidence.

Most vortices wouldn't be able to cross a body of water - they would suck up water into their vortices... diluting the acid, melting the ice, dousing the fire, or effectively grounding the lightning. If any vortex were going to be able to cross water, I'd suggest only lightning, since you could say that a lightning vortex would work like a storm, and thus already have water in it. The other types would undoubtedly be destroyed by passing over water.