Fluctuating Idle

I just bought a used 01 Honda Civic LX with 62k miles on it. (1.7L automatic trans)
Everyday I seem to notice a different noise but overall the driving seems okay.

First off: 4 days ago I could hear the engine slightly revving at idle. It hasn't happened since BUT every time I stop it idles anywhere from 1000rpm to 500rpm steadily. Is it normal for it to be 700 on one stop then 5 minutes later be 500rpm at another stop?
Also, I can feel a lot of vibration in the body of the car 80% of the time, even in the brake pedal! Is this motor mounts? Or maybe some sort of idle adjustment like my older volvo had?

Next: Every morning when I start the car and turn on the A/C there is a weird almost growling noise for 2 minutes. The air also isn't cool after acceleration. It runs okay besides those 2 things. Is it the compressor maybe? The belt looks like it had been replaced.

Also: the brakes. I know they need new pads and shoes but I may need new rotors. When I am stopping sometimes it jumps down, like it's going to hit the floor all the sudden and acts like I slammed on the brakes. And when I'm at a light it will drop too. Like air being let out. Slowing down isn't smooth at all but there's no noise (squeaking or grinding), just vibration in the pedal.

Thanks so much!