Why is the O2 sensor burning?

Try replacing it a second time. You may have just been unlucky and got a defective one. Unfortunately it happens. Hope that helps! Jim

Is your car running way to rich or too lean?

I replaced it a second time, and the AC worked for like 10 minutes and the temperature gage was also working then all of a sudden the gage went back to the cold and no more AC.

Sounds like a problem with the coolant temperature sensor, not the oxygen sensor. When the coolant temperature sensor is disconnected the computer will assume the engine is overheating. The air conditioning will shut down and the temperature gauge will stay on cold because the coolant temperature sensor is unplugged. Also, your radiator cooling fans will run on high speed and the check engine light or service engine soon light will come on. Check the wiring going to the coolant temperature sensor. Make sure everything is in good shape and the sensor is securely plugged in. Hope that helps! Jim