Car has squeeky belt, shuts of when compressor kicks in and is in idle

Sure sounds to me that you have a siezing or binding compressor. That's why the belt squeals and the engine stalls, I think. It could be also that the expansion valve is not working right and putting too much load on the compressor. also check that the condenser fan in front of the radiator is coming on with the compressor, that will cause the system to overheat if it's not OK. I recommend going to a Mazda specialist or an A/C specialist for help. If the compressor is working too hard it will break down with the heat and pressure and may have done so already go don't use it for the time being. Here's a directory link for you for Mazda: http://repairpal.com/mazda-repair-in-north-miami-beach-florida