Would really old Anti-freeze plus low levels of anti-freeze (below minimum mark) cause the heat sensor to turn off the a/c?

What 'heat sensor' are you referring to? Temp. sensor for gauge? IF reservoir is below 'min' mark , but not empty , radiator should still be full(no air pockets) , when COLD , remove radiator cap and verify. I'm not familiar with Suzuki 'Aerio' , so if it doesn't have a radiator 'cap' on the radiator , then the reservoir is pressurized and needs to have coolant 'topped off' when cool , and monitor for leaks. Is it overheating? Or is the A/C simply not working?