I just bought a car Friday from a used car dealer, now I'm having major problems with the alarm and ac.?

I bought a 2005 VW Jetta from a used car dealer in North Carolina Friday. When I test drove the car the alarm went off a couple of times and the dealer assured me I was just accidentally hitting the panic button. Now it's Tuesday and I'm definitely not hitting the panic button. The alarm goes off if I so much as think about touching my keys, and then, this morning it was just sitting in my drive with the keys on the hook by my door and it starts to go off for no reason at all. The trunk release and unlock/lock features on my key also do not work, but instead set off the alarm. I also raised a concern that the ac wasn't cold when purchasing the car, but was told that it was probably just from where it was sitting. Yesterday we had a very warm day and the ac didn't work. When I called the dealer he said he would fix it covering 100% of the costs, if I waited 30 days to report it to the warranty company and told them that it did work when I bought it and it stopped working. He said he would but the ac part in writing for me, but I've become really concerned. I'd like to go to the dealer today and confront him, but I'd like to know a little about my rights first. (I do have a 2-year warranty).