A bad alternator will cause a battery to go bad. It does not have an effect on the air conditioner.
Yes it can cause bulbs to blow.
Probably leaking freon.
A bad alternator will cause the fan blower not to work properly. Have the alternator tested!
Your A/C needs recharged.
Max
You have a vacuum source at the intake manifold that is possibly disconnected.
The most common cause would be low refrigerant.
Compressor not running, blown fuse, low of freon.
over-charging...great way to blow up the compressor...
absolutely because if the compressor is not engaged then it can not produce cold air.
An air conditioner blows out heat
you would need to add freon