A/C Problems! (screech sound)

A/C isn't designed to be ice cold when you first start the car ( a heater doesn't even do that). Allow the system to warm up to work properly. The screaming sound is from a loose belt. Change your belts and then remember the car has to be going down the road and operating in order to have best results. It's not designed to give ice cool performance when sitting around.

Your a/c compressor is locked up, the burning rubber smell is your serpentine belt sliding over the a/c pulley while the clutch is engaged. You need a new a/c compressor.