The Mississippi Queen is a single coil, it will pick up interference from evey electrical item in your house, from the fridge to the hoover but the worst is often a TV or computer. This is one of the reasons that humbuckers were invented! Try moving away from computer or turn it off if you're not using it, or else you'll need a noise gate like the Decimator pedal.
The amp clunk sounds like an amp problem, I can't imagine any sound like that being caused by the circuit in the guitar, especially if the guitar volume is at zero.