Hey Granger - congrats on your purchase.
Sounds to me like you may have bits of a hands free car kit like the nokia CK-7W fitted to the car by a previous owner. They often give a (normally quite loud) boop noise after approx 10-20secs of ignition on.
Best way to check is if with your mobile - turn on bluetooth and scan for new devices - you may well see some sort of hands free come up.
Know nothing about the MINI sat nav system so will bow to others knowledge on that front. | 
