Yes, but most people aren’t neutrally buoyant. Most people are a little less dense than water, and so have a maximum depth their buoyancy will allow them to reach starting from a jump.
I think this also addresses your other questions, since I was assuming a positively-buoyant person for them, too.
EDIT: Oh, and I was also assuming a constant-density person. Given that we’ve got lungs full of compressible air, that probably isn’t a good assumption.
