I’ve been reading how microwave ovens cook food by spinning water molecules and was wondering if water is the only molecule that can be spun using microwaves, possibly by raising or lowering the frequency? Could microwaves even spin single atoms (like hydrogen or carbon)?
Don't get caught up in the physical meaning of "spinning" here. The simple explanation is that the frequency of a microwave oven is chosen so that it matches the resonant frequency of one of the water molecule's vibrational modes.
So, for a different molecule or material, if you know the vibrational modes, you can select a microwave frequency to match and thus transfer energy into the material. Of course, some molecules or atoms may respond to much higher or lower frequencies.