How do I avoid squeaking with a hardwood floor?
The underlayment being nailed down was the first mistake.  Nails pull, wood slides against the metal, and it squeaks.  Subflooring (all of it) should be screwed down (and glued, preferably).

The bounce is probably a problem with the span of your floor compared to the thickness of your joists.  Was the floor bouncy before the hardwood install?