Is it normal for a PT Cruiser to cut out and almost die when running air condition or heater?

Normal? Use common sense. Who would buy a new car that did that? More likely the battery was recently disconnected or run dead and the previous owner didn't know how to fix it. If so, the Engine Computer lost its memory and has to relearn "minimum throttle" before it will know when it must be in control of idle speed. It also might not give you the normal "idle flare-up" to 1500 rpm when you start the engine. To meet the conditions for the relearn to take place, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the brake or gas pedals.