May need to be recharged.
Chances are your air conditioner is low or out of coolant. You can go to AutoZone, Napa, Advance Auto, or numerous other do it yourself car repair stores and have it checked out.
no
A failing throttle position sensor will cause idling problems when the car is warm. The failing sensor can also cause the car to stall when idling.
by the idling air control valve
how do you know if the air conditioner in your car works in the winter
Blowing cool air while idling & the water pump is not moving very fast is a key indicator of low engine coolant levels. Add some anti-freeze/water and likely you'll have warm air all the time.
moving
An air conditioner in a car uses quite a bit of power. It is not unusual for a car to hesitate when the AC comes on.
Yes. If the engine is running too warm, from a lack of coolant, the ac will not work.
You will use more gas when your air conditioner is running.
Yes, it can.