Am I compensated by the electricity company for electricity that exits my home on the neutral wire?
You are not really paying for the electrons that move in the wire, you pay for the force that moves them. It is like cutting a board with a hand saw. You push an pull it to cut the wood using the same teeth for each stroke. The electric company pushes and pulls the electrons and the moving electrons do useful things like provide light. You furnish all of the materials including the electrons in your wires. The electric company sells you energy in the form of moving electrons.