House humidity ranges between 35% in the winter (I have a whole house humidifier but it does not seem to work very well) and maybe 45-48%% in the summer. Is this ok? Oak floor has been in for the life of the house and apart from some squeaks it seems to be holding pretty good.

That sounds good. Manufacturer should also provide humidity guidelines with the installation instructions. High humidity is the big problem causer. Also, keep your basement at a good humidity level too as a humidity imbalance between above and below the flooring can cause problems.

Great. Basement is finished. I guess it should be no problem.

Ok. So here's a couple of additional questions. Subfloor is 3/4 in OSB. All floor will go over a finished basement (Basement ceiling finished with drywall). 14 years old house.

1) Should I use some additional underlayment (Like Rosin Paper)? Is it really needed?

2) Nails or staples? What air pressure? Wood is hickory.

Thanks!!

Use a vapor retarder between the subfloor and hardwood flooring. Aquabar B is a good one.....available in HD. Don't use Rosin paper.
The Cleat vs Staple debate has/will go on forever. What do the flooring manufacturer's installation instructions recommend? Staples are cheaper but can cause more tongue splits if you aren't careful.
Do a test to determine correct air pressure.