I would play it cool for now. I'm with Mini - say you need AC and if they don't fix it you will need to find somewhere else to live, but I wouldn't start withholding rent just yet. If this lady is as shady as she sounds, I wouldn't be surprised (in the event that you anger her) if she waits for you to leave one day and changes the locks and then where does that leave you? Out $200 and all your belongings as well.
Maybe offer her half of December's rent until the AC is fixed, at which point you'll either pay the remainder or move halfway through the month; if it doesn't get fixed, stay out the month, don't pay the remainder as a way of recouping that deposit that seems all but lost, but relocate your valuables to a friend's house just in case!
Maybe offer her half of December's rent until the AC is fixed, at which point you'll either pay the remainder or move halfway through the month; if it doesn't get fixed, stay out the month, don't pay the remainder as a way of recouping that deposit that seems all but lost, but relocate your valuables to a friend's house just in case!