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?
Probably both - things that spark usually radiate radio frequencies, and ordinary brushed motors typically spark at the commutator; the combination of an inductive load and frequent switching as the coils are turned on and off will induce voltages on the supply lines. That's how I see it , anyway. Voltage fluctuations on the motor supply lines could be measured with a scope. RF radiation could be measured using a specialised RF power meter (I've never seen one, but I'm sure they exist) or by testing how close your electronic equipment can be before it is affected. RF signal strength follows the inverse square law so you can estimate relative power from changes in the distance at which an effect is noticed. In any case I guess your goal is to get rid of the effects rather than put a number to the problem, so as long as you can make the symptoms go away that's probably all that matters.