Wow.
California, right? Aren’t there building codes and inspectors approving the project step by step - after the project coordinator/contractor pulled the appropriate permits?
I agree with all your concerns.
The horizontal supports can’t be held to concrete with nail gun nails - that’s absurd - they should be set into place with caulked construction adhesive then supported with concrete screws (which are chemically treated to prevent corrosion) driven every 16" if there will be a load (books, etc).
1" x 1" strips are not much more than furring strips and certainly shouldn’t be used in that application.
I think I follow you on the method of shelving (sliding one against the other) and it does not sound like a structurally solid approach.
Again…wow.