Step-by-step explanation:
yes, correct, from the batteries, wires and bulbs. in short, from everything that is part of the circuit.
electricity is just a push on mostly already existing electrons to move along.
a battery has a surplus of electrons at the "-" pole, and an electron deficiency at the "+" pole. that creates an electromagnetic "pressure" (voltage), the surplus (ampere) squeezes into the circuit, while the deficiency pulls like a vacuum, and all that creates an electromagnetic field around the whole circuit, which moves also the existing electrons, pushing/sucking electrons at the end of the circuit "chain" into the "+" pole.