Proper Orientation for Plywood Subfloor under 3/4" Hardwood

I recently purchased a house in New Jersey and the 2nd floor was filled with old carpet that we wanted to replace with hardwood flooring. I ripped up the carpet only to find particle board under all of it. I proceeded to remove all the particle board to find the 5/8" (19/32" really) CDX Subfloor over 16" OC Joists. We are looking at a rather expensive hardwood so I want the installation to be ideal so I'm going to add a 2nd layer of plywood underlayment over the existing subfloor. Here are my questions:

1. What thickness underlayment should I use. The top step of the stairs is currently 1" lower than the rest so 1/4" plywood is not a problem but should I put 1/4" or go to 1/2" to make sure that the floor is stable with over 1" of subflooring under the hardwood.

2. What type of plywood should I use CDX? BC Sanded? etc.

3. The house is 'L' shaped due to a renovation done in the 90's. The front of the house (short leg of the 'L') has the joists running E-W and the back of the house (long leg of the 'L') has the joists running N-S with the subfloor running perpendicular to the joists in each leg. At the line of the renovation the subfloor is cut and turns 90 degrees. Because of the look we are going for we would like to run the hardwood flooring perpendicular to joists on the long leg of the house which would then run parallel to the joists in the short leg. Should I run the underlayment all in the same direction or match the subfloor and cut it at the renovation line? Is there going to be any issue at the transition point or something I can do to stiffen that line up (it's only an opening at the top of the stairs for the hallway approximately 4' long, everything else is under a wall)?

4. How should I attach the plywood underlayment to subfloor. I was told by one of the hardwood installers to glue and screw (or ring shank nail would be allowable) to the joists. Or I've read that I should not attach the underlayment to the joists and avoid them and attach underlayment to the subfloor using staples spaced tightly (Every 6") around the perimeter of each underlayment sheet and scattered around field?

Any help is appreciated as I want to get this right the first time. Please let me know if you need any other information.