As to question one. It is hard telling. Codes could have changed, that is what the builder could have been used to, it could have been designed for a higher live/dead load than the rest of the house (the modern tables I quickly looked at say you are at least 2x10 at 16" o.c. to get a 17' span @ 30 lb/ft2 live load), it could have been designed with lower deflections "L/###" to accommodate different flooring options, or it could have been something previously and that was what was already there.
As to question 2, I would drive the nails back down, and add in good quality screws (drywall screws are not very ductile and can snap, and structural screws are closer to nails in ductility. Since you already have nails for structural I would just use a good quality wood screw). I would go with at least 1-1/2" as I like screw to have at least 3/4" of bite (but I often exceed that). If I was laying the subfloor for the first time, or had it removed for some other reason, I would nail (for structural) polyurethane glue to the joist (kills squeaks) and screw (acts as clamps for the glue). You might be able to tell I can go a little overkill.
Also I see no need to remove the old fasteners Unless they are causing you issues. I am redoing a bathroom and after removing the tile I have found 1 layer of 5/8 ply nailed. I am going to drive the nail back down, add 3 in exterior (peace of mind in wet area) screws (I have lots left over from deck building), add a second later of 3/4 ply glue to the first and screwed with 1-3/8 exterior screws avoiding the joists. Then build by new floor on top of that. There are 3 structural supports in the bathroom; exterior wall, beam under the bathtub, and load bearing wall under the oppsitite wall of the exterior wall. (the room is 11 feet wide) And the whole house is framed in 2 x 12 for the floor joists.