The original 2x4 that rested on the floor was removed in one piece with approx. 7" of the vertical studs attached to it. The sides of the studs rest against a concrete block wall. The removal was done to allow access to the cold joint for the application of a waterproofing material whose surface is varied and uneven. Now I'd like to install a new 2x4, hopefully with closely matching 7" studs attached to it to be sistered in, since all the original studs were partly rotted from flooding. I can't drill down into the concrete floor because it would disturb the waterproofing, but need something to serve as "shims." I'm concerned about using construction adhesive of some kind since I think I need more time to do the fitting even if I check everything first.
If I'm interpreting correctly, your framing isn't so much structural as a place to hang drywall/ whatever. If this is the case, then a bunch of construction adhesive will do fine. If you can, add an "L" bracket or two to the wall to tie it all together.
Pressure treated wood is probably what your AHJ would call for in this setting.
The way I'm picturing your question is that you are trying to level a 2 x 4 floor joist; specifically the one that runs parallel to the block wall. On it will rest the studs that make up the framing for the finished wall? If this is the case to shim the joist level with the other floor joists purchase plastic shims at any lumber yard or home center. Just like wood shims, but won't rot or swell from moisture and the serrations make them easy to snap. Another material for shimming damp environments are roof shingles. Lastly, to splice in stud sections to replace the pieces that were cut out, sister in the new piece and screw gusset plates of the same dimension to either side of the new section.