How can I stop cracking/squeaking sounds while leveling this floor?
Most any material that keeps the wood to wood contact to a minimum should work. The most common material used is red rosin paper, but asphalt paper used to be an old favorite. I would avoid any thick absorbent materials like untreated felt or open cell foam, as they can absorb moisture or water and become moldy.
Use screws whenever possible instead of nails, as nails will squeak as they become loose as wood shrinks around them.  If you have to use nails, be sure to use threaded/ring nails to minimize this potential problem.