I have done similar things to other devices, so I can give you a rough outline of what to do (assuming you are in the USA). By law, anything that transmits/receives a wireless signal must go through FCC testing, and what I have seen is they usually make this a card with a standard I/O port (much easier to get one card through the FCC process than a bunch of them). Look up the "FCCID" in the owners manual, and you can go to the FCC website and find exactly what you are looking for. The next thing you need to do is actually find it, and that will probably be the most painful part. But once it is found, you can simply remove it.

I had to do something similar to a sound system I owned. For some reason, they added Bluetooth with absolutely no authentication, so anyone in range could pair to it. I just removed the Bluetooth adaptor (it uses I2C and/or SMBus to communicate with the rest of the system).

Yes. It varies from car to car, but as someone with a new GM vehicle I can say it's definitely feasible to disable OnStar. And contrary to what someone else up-thread suggested, it throws no codes if you do.