Q: I have a 2015 wrx, my AC compressor pulley spins a few seconds then stops for a few then repeats, and makes an odd sound.

The cycling of the AC compressor is normal as the compressor cycles on and off. You may also hear a bit of a change in the exhaust as this happens. The computer will automatically compensate for the additional load the compressor puts on the motor by adding additional fuel to the motor. With regard to the vehicle not starting intermittently, this may be related to a number of things, but if the motor eventually turns over it is likely that the problem is not related to the battery or charging system. I would suggest checking the starter relay as this may produce the symptoms you are describing. The starter relay directs power from the battery to the starter solenoid which then engages the starter when you turn the key. When this is not working properly, you may notice intermittent starting problems including no response when turning the key to start. Generally, when this does fail, it does so very randomly and usually without warning other than intermittent starting. The power from the battery will still power other accessories such as radio, horn, etc., but you may not have any power to the starter. I would recommend having an expert from YourMechanic come to your location to diagnose and inspect your vehicle.