The subfloor in the house is currently 1/2" Plywood Sheets. I though I read that 5/8" or 3/4" plywood subfloor was recommended for hardwood. If that is the case I could add another layer as underlayment. Obviously want to keep the height to a min so not sure if 1/4" or 1/2" would be suitable.

Also, I can either add more nails or screw down the existing 1/2" subfloor to the joists. Is screwing preferred over the spiral flooring nails? Want to make sure the floor is as solid and sound as possible.

just mark out the beams and nail the flooring directly to the beams and in between...

one on the beam,one in between..

pre-screwing or nailing is fine...but you will be doing that in one step in the floor install

of there is obvious weak or squeaky areas, by all means..secure it.

So can you add 1/2" plywood to an existing 1/2" plywood subfloor to make it meet the minimum requirements of 5/8" under a hardwood nailed floor or not?

yes sir you can. I would run screws into them myself get you one of those quick drives and you can get it done fast.

And run that plywood across the other plywood, not the same direction as the other plywood, keep in mind ,now you got an inch of subfloor, flooring goes any direction you want it.