Flooring – Finishing Attic Floor (Joists Blocking / Insulation)

I moved into a house built in the 1920's several months ago that has a finished attic where the former owner's two teenage boys were living. I want to go from the old ratty carpeting to nice floor laminate for a yoga studio for my wife.

I assumed the subfloor beneath the carpet was the original old floor paneling that exists in the remaining unfinished part of the attic because walking around produces a lot of squeaking and noises. Upon removing the carpet I found my suspicions confirmed, so I will be removing the old ancient floor boards and replacing with 4' x 4' tongue and groove OSB boards. Upon starting to remove the original subfloor I saw that it sat on top of 2×6 ceiling joists without any blocking or cross bridging so I plan to add blocking for extra structural support.

There is also loose fill insulation under the current subfloor that looks like it's been partially removed over time and or was just never blown in to fill the joist space.

1. Can I screw the blocking instead of nailing it as I'm a little worried the nailing might cause cracking in the plaster ceiling (with wood lath) below?

2. Is it okay to sister a 2×6 board to the current 2×6 board along the front and back perimeter of the finished area to support the ends of the new subfloor since I'll be cutting the current subfloor back to the edge of the current 2×6's? Can I use screws instead of nails?

3. Should I replace the loose fill insulation with unfaced batts and fill in any small areas with the old loose fill?

4. Does all of this sound kosher / is there anything else I should be considering?

Here is a picture of the current space and a simple diagram of what I want to do.