Number of capacitors for a DC motor
For EMI reasons. Your cable is an inductor at high frequencies but also an antenna and you don't want to nor are allowed to radiate away radio emissions from your (brushed) motor. You want to form a Pi-filter, where the capacitor on your source forms one leg, the inductor (wire) the horizontal bar and the capacitor straight on the motor the other leg. It might take a bit of imagination but that's a Pi-sign. If your souce is already a battery or power supply, you already have the first part.


As for 2 and 3, you may be able to filter out very high frequency emissions this way. Just don't waste large capacitors here since you need them across + to -. You will probably be in the 100pF to nF range for 2 and 3, if any and depending on how the motor is grounded.