Why is it important to make sure that miners spend money (on electricity) while mining?
They are incentivised to mine via the blockchain protocol.
By not following the protocol they can lose their investment as a miner as mining against the protocol will not work within the blockchain protocol.
Why would it be very difficult for someone to go back change a previously added block?
Due to the blockchain hashing algorithm , to re-mine a previous block will break the chain in the blockchain for which then you would have to re-mine blocks whilst other miners have already mined those blocks making your version of the blockchain invalid as the longest chain wins. It would also be very costly and most likely impossible as the current blockchain algorithm is extremely secure.
How does the network regulate mining difficulty?
Difficultly rate is adjusted every 2016 blocks.
Blocks need to be mined within a 10-minute interval.
If the hash rate increases (more miners) so does the difficulty. (nonce target lowers)
If the hash rate decreases (less miners) so does the difficulty. (nonce target higher)
The protocol will adjust the difficulty rate to make sure blocks are mined every 10 minutes.