I'd continue looking for another used FRS or even a BRZ.
The dealership lied to you because as others have said it has been rebadged with Toyota emblems. It's really a Scion FRS. Who knows what other lies they may have told you.
The Invidia N1 exhaust is LOUD. Your neighbors will not like you.
No need a cold air intake. Just buy a drop in air filter like Perrin, Cusco, Apexi, etc. Dry air power filter is good enough.
Just my 2 frickin cents!