2002 AC and Radio

I just got me a 2002 Cavalier I love it BUT my AC seems to not want to work when i turn on the blower the engine idles really ruff to the point it will die but not all the time. The AC wont work at all any body else have this problem?? Also stupid thing to ask but I like the way the CD player stays on until i open the door but thats the only reason I want to keep the stock head unit will that still work with a Pioneer head unit??