OK, no problem...
GPS: it will only work on the surface but it will give me a referenced location (IMU is not referenced and will drift w/ time)
Dive and Resurface: The whole unit is VERY SLIGHTLY (a couple of grams) positively buoyant with the cg slightly below the center of buoyancy. This allows the whole unit to "fly" like an airplane in all three dimensions.
Yes, the only down side to this design is you do have to be moving in order for it to be controllable. It is designed to go places fast and explore not pick things up and bring them back to the surface. As for turning radius... I have no idea, it will depend on speed and I haven't tested it in a bigger space than a bathtub yet. The motor is reversible though so turning radius should not be a huge issue.