1. Why is it important to make sure that miners spend money (on electricity) while mining?
If it was cheap or free then there would no punishment for going back and attempting to change previous block data, introduce false transactions or break any other rules. The miners need to recoup the costs of mining which can they can only do if they follow the rules and secure the blockchain.
2. Why would it be very difficult for someone to go back change a previously added block?
any slight change to the data in a block would change the hash of the data in that block, which would change the hash for that block, which would change the hash for every block after it and invalidate the addresses that they point to. Every block after (and including) the modified one would need to be remined so that the hashes all point to each other and are valid, and this would have to be done at a faster rate than the unmodified chain, as the unmodified chain would be multiple blocks ahead of the modified one. Therefore this could only be achieved by having more than half of the mining computer power working on the modified chain (51% attack). It would be more cost effective to have all of that computer power focused on the original chain, as that share of the computing power would earn the miner more in rewards than reversing any one transaction could.
3. How does the network regulate mining difficulty?
The hash of any mined block must be below the difficulty target. The more miners on the network the lower the difficulty target of the block hash, so the chances of getting a hash below the target are reduced. The lower the network hashrate (miner computing power) of the network the higher the difficulty target, increasing the likelihood of getting an acceptable hash for the block.