Bulbs have resistance . Adding more bulbs in series increases the resistance. Adding more bulbs in parallel decreases the resistance. The greater the compass deflection, the greater the current. The brighter the bulb, the greater the current flowing through the bulb.
Electrons are what actually move in a circuit.
I like to think of the electrons as being repelled out of the negative end of the battery and attracted to the positive end of the battery. This allows me to determine which way the electrons move. The electrons move to one of the two plates and stop. They repelled electrons on the other plate which causes electron flow to continue through the circuit. As the electrons pile up on the first plate, those electrons will repel the next few electrons that arrive there.