Loud noise started, noticed coolant leakage shortly after

About a month ago, the serpentine belt came off while I was driving. I got the belt replaced, a week later my heat goes out, so I added some coolant and the heat started working again. About a week ago, I started the car and I usually have to let it run about 5 mins before taking off or it'll die as soon as I try to pull out, but I notice a new noise. I pop the hood and notice that one of the pulleys is wobbly. I need to know if the pulley is bad, or if it's the water pump connected to that pulley. Also, my A/C does not work and I've done everything to try and get it to work. Any advice would be appreciated.