Best approach for squeaky subfloor fix, with some water stains
When I redo flooring, I always remove all the nails, and then screw the subfloor down.  It costs nothing but time, and I'd rather waste time doing it, than have a squeaky nail after the flooring is on.

As for the water marks. It does look like there was some water infiltration, but without poking around it's difficult to say to what extent.  Replacing the siding could well solve the issue, depending on where the water came (is coming) from. 

If there were animals in the house, the "water" stains could be from poorly housebroken animals.  If you notice an odor, you might want to paint the subfloor with some Kilz or similar primer. If it's really stinky, you might want to treat the stains with an enzyme type cleaner before priming.