I do not think it is possible to create air spots underwater now, with a fixed sea-level plane where every no-hard block under the surface is filled with waterblocks, but maybe when the new lake/river mode arrives.
At the moment the only underground system that not fills with water is the cave-system, could probably use that to create underwater-system, and with right noise make some good worlds.
Interesting idea, i see if i can test it.
No, they are not hollowed out. Its only high-maps so they solid.
Its up to they who wants to dig out their own flat.