Why is it important to make sure that miners spend money (on electricity) while mining?
Requiring miners to use much electricity (and often much money) to mine BTC, increases the degree of incentive for miners to do their job and to follow the BTC network rules. This way. if they do their proper work, and follow the rules, they get valuable BTC. If they fail to properly do their work and if they do not follow the rules, they risk losing their invested resources of electricity, and for many miners (if they do not have a free source of electricity) this results in them losing money. Since miners are likely to want to gain money instead of lose money, the requirement of using a lot of electricity provides good incentive.
Why would it be very difficult for someone to go back change a previously added block?
Because they would need to not only change that block, but also change every block which came after the changed block. This would require mining all these blocks again, which would be very expensive. It is also not likely to happen in the real world, unless they controlled the majority of the BTC network. A single computer, with today’s technology would require very much time to mine all the new blocks again. Also, the BTC network chooses the longest blockchain as the correct one. This makes the task of replacing the blockchain even more difficult, since the majority of miners continue to add to the same chain as before, and as the blockchain becomes longer, there are more and more blocks to replace.
How does the network regulate mining difficulty?
When there is more computer power, or more active miners, on the BTC network, the level of difficulty is increased by requiring block hashes to be lower and lower, in comparison with a target number (which becomes lower to increase difficulty). Since there are few numbers between zero and a particular low number, this low number provides fewer correct answers available for solving the BTC mining problem. Mining computers guess again and again, and many hashes are higher than the low target number. Therefore mining computers generally need to provide more guesses about the correct nonce, to get a hash which is low enough to be less than the target number.