It is very easy to cut through the whole wire. It might help to make a very shallow cut, then twist and pull off the insulation. The battery can starts electrons flowing only if all parts of the loop are connected. If any part of the loop is disconnected, the circuit of electrons in the loop is broken. The wires are coated with plastic to prevent short circuits and electric shocks.
Electrons flow out from the negative end of a battery into the positive end.
When the battery is turned around in the circuit, electrons will flow the other way. They will flow through the bulb holder in either direction. The light gets brighter with two batteries. Use magnifiers to examine the filaments inside different light bulbs. Make enlarged pictures for display.