Solid Hardwood, Engineered and Laminate Flooring - Subfloor Prep for Engineered Hardwood Floor

I've removed all carpet and padding, as well as pulling up all tack strips and staples (from the padding being stapled to the floor). I plan on hammering down any subflooring nails (the ones attaching the subfloor to the joists underneath) that may have started to come up and vacuum the subfloor. Is there anything else I need to do before starting on my hardwood floor installation?

Screw down the subfloor, and pull any lose nails that will promote squeaks.

A straight edge to check highs and lows, especially the seams in the subfloor panels. They can sometimes peak up, you will need to sand them flat.

So everywhere there's currently a nail attaching the subfloor to the joists underneath, I should put a screw in? That's to furthur prevent the subfloor from coming up? Do I need special screws? I currently have a whole box of nails that are "self-drilling" (the end of the screw kind of looks like a drill bit), and I believe the box reads that they can be used for wood applications. Would that suffice?

In addition, if it looks like any nails are currently starting to come up, I should just remove them?

Thanks!