If you are trying to squeeze extra inches then use 2x3 studs instead of 2x4's. You don't need to attach them to the wall at all. If you can, frame the wall "on the flat", meaning flat on the floor, as this is fast and easy if you have enough room. The wall only has to be attached every few feet through the top plate into the floor joists above. Use a cement nail or powder actuated gun to put a nail in every 2nd or 3rd stud bay into the concrete floor. I normally frame the wall to be a total of at least 1" shorter than the actual height of the floor because invariably it can be difficult to stand the wall up. You need to measure all along the existing foundation wall to find what is the shortest point. Then, just put a few shims between the top plate and the joists and put a spike or long screw up every few feet.
I would use 2" of foam insulation, I like the foil faces "Celotex". You want to leave at least a 1" air space between your wall and the insulation. I always use pressure treated wood for the bottom plate. drywall is typically put on the wall, top piece first, after the ceiling drywall is up. Then leave the bottom up off the floor like you said. Assuming you will have some sort of baseboard you could leave the board up between 1/4" and 1" off the floor. This isn't that critical because with baseboard it won't show. The concrete floor probably varies so to try to leave a precise, even gap will take more effort than it is worth.