Hi,
I have a parquet floor which I am removing to install hardwood flooring (3 1/2 x 3/4")
As shown in the pictures, when I am removing the flooring, the glue is so strong is some areas that it pulls off some of the plywood underneath.

My question is:
- Should I remove the plywood given it has pits and valleys or should I try to fix them somehow? (if so, how?)
- The plywood is installed on cement with nails - if I remove the plywood, do I need a special tool to install nails into the cement flooring underneath? What type of nails would work?
- Lastly, if the best solution is to remove the plywood, should I just try pulling it out now with the remaining parquet still glued on? Is there a proper way to remove all this stuff?

Thanks so much!