Wow, that's a lot of ground to cover!
Yes, there are spiny lobsters here. I've never seen an American lobster, but that doesn't mean they aren't around. My guess is that if they are here, they would be north of Cape Hatteras, where the colder water is.
Yes, you can catch the spiny lobsters. No, I don't know the regs, other than the fact that you have to bring them in without any holes in them, and no egg-bearing females. There are also slipper lobster here too, and they're not bad either. Most common places to look for lobsters are the deeper (90ft +) ledges, which means a bit of a boat ride to get there.
There aren't a lot of great shore dives in NC. Two of the most popular are the "triangle wrecks" in Kitty Hawk and Radio Island near Beaufort.
Yes, the sounds are safe for small boats. Best to watch the weather carefully though, if you're heading out in Pamlico and Albemarle sounds. Because of their size they can get rough pretty quick. The sounds are generally kind of silty, and I don't know anyone who dives in them on a regular basis.
For a diver, the places that offer the most variety are the Morehead City / Beaufort area or Wilmington.
Hope this helps. You might also want to try
www.ncdivers.com for more great info about diving in the area.