Hardwood install and underlayment

Q: Question: I want to install a 3/4 X 3.25 red oak hardwood floor (nailed). My current flooring is 1/2 non TG plywood over 2X8 joists at 16″ with a 5/8 particle board underlayment on top. I will remove the particle board and replace with: 1) What is the best hardwood flooring underlayment? 5/8 or 3/4 ply or OSB screwed to the 1/2 ply?

2) Is there any reason NOT to also glue to the 1/2 ply for a more rigid floor?
3) Is there any reason NOT to screw the new underlayment into the joists for added rigidity?
4) If ply, should the underlayment run parallel, but seam offset from the original 1/2 ply or perpendicular to the 1/2 ply?
5) Also, I need to run the hardwood in a hallway (3′ wide) parallel to the joists (in this case they are doubled 2×6 joists). What should the underlayment be in the hallway and how should it be oriented to the joists?

A: I would always choose plywood over OSB. 3/4 thick is significantly more rigid than 5/8. Since you are going over 5/8, you may decide to forgo the extra cost of the 3/4. Height issues may make a difference in your decision.
I am not aware of any reason NOT to glue the 2 layers together. Make sure the 1/2 is dry and acceptable to install a floor over top.
You should absolutely try to screw the new underlayment into the joists. This will secure not only the top layer of ply but the half inch also, in case it has not been well secured. I would install the new plywood in the opposite direction than the 1/2″.
If I remember correctly, the NWFA guideline for installing perpendicular to the joists is 1 1/4″ thick subfloor. If that cannot be reasonably achieved, I would make sure the existing subfloor is securely screwed down and then nail and glue (with a polyurethane adhesive) the hardwood floor. As an alternate, you could install the floor on an angle, but the amount of work involved in doing this, especially in such a small space hardly seems worth the effort.
I hope that helps.