1. Is that noise in the wire itself, or in the air in the form of RF which is passing through the wire shielding and corrupting the flow of electricity?
Its not just RF that get emitted from a motor, you also get EMF. Since all electric motors use coils, they can and do emit EMF. That EMF can cause voltage fluctuations to surrounding electronic devices that are not properly shielded. Simular to a magnet passing over a wire going from a battery to an LED. The magnet will either dim or brighten the LED depending on the direction and strenght of the magnet. If your getting noise on your nearby electronics then you might want to look into adequate shielding. I wonder if those couplers you find on VGA cables will help shield your wires.