Why is it important to make sure that miners spend money (on electricity) while mining?
Because it incentivises miners to play by the rules, otherwise their block will be rejected and they will lose money.
Why would it be very difficult for someone to go back change a previously added block?
Because they would need to re-mine every block after and in theory would need to become the longest chain.
How does the network regulate mining difficulty?
Difficulty is regulated by the hashrate on the network.