Replacing heated tile with vinyl plank

Hello, in my bath remodel we are replacing a heated tile floor with vinyl plank floor. After removing the tile, heating elements and the tile backer, there is about 3/4" difference between the subfloor and the hardwood floor at the doorway. My vinyl looks to be 3/16" - 1/4" thick, so I'd like to put a 1/2" thick second subfloor under it to make it roughly flush.

I'm replacing a section of the subfloor where there was a leak and there had been rot. The rest of the subfloor is in good shape, except a couple of the seams are matched maybe 1/4".

Questions:

1. I assume adding an additional 1/2' layer of subfloor is OK, right? Does it matter what type of sheet should I use?
2. Should I be concerned with the mismatch in the main subfloor and if so how do I address it? My intention is to make sure my new 1/2" panels bridge those gaps and no seams align.
3. Should I use screws or nails to put the new subfloor down and what spacing?

Thanks!

 

When I lay new 1/2" plywood down as an underlayment over the old subfloor, I typically lay down a layer of felt then screw it 12" on center. No glue.