- Why is it important to make sure that miners spend money (on electricity) while mining?
The idea is that miners are incentivised to work and solve the cryptography challenge in order to add their block to the blockchain. The way they do this is by computing power which consumes electricity. If they try and cheat they will have spent a lot of money on energy for no reward - Why would it be very difficult for someone to go back change a previously added block?
Blocks are linked by creating a hash which accounts for the transactions in the block, the previous hash and a nonce (random number). If someone tried to change a transaction in an earlier block the hash would be different and that would invalidate all following links - How does the network regulate mining difficulty?
The system uses a difficulty level based on the number of miners hashing, the nonce will be more difficult to guess the higher the number of miners, Miners will need to calculate a nonce that approaches 0 rather than a higher number approaching infinity
- So that they are incentivised to follow the rules and receive the reward to cover their electricity bills as well as earning a profit
2.As this would affect the links that have already been formed(the hashes) and one will have to solve cryptographic puzzles again to reform those links (which will take them hundred of years of time). Additionally, other miners will also mine many new blocks which the person will have to reform all the links.
3.Mining difficulty is increased when they are more miners, and this is done by lowering the target.
Miners donât spend a lot of electricity to speed up mining. The reason why its important for them to spend the electricity is because that ensures that there has been actual work put behind a block. Meaning if anyone wants to go back and change a block, the only way to make the block valid again is to spend the electricity again. This way we connect virtual information on the blockchain with the real world. So when people say that bitcoin is not backed up by anything, we can be sure that they have no idea how bitcoin works at the core. 
Correct. In bitcoin, this adjustment is made every 2016 blocks. 
Proof of stake is a different consensus algorithm. As you said, miners best approach is to be honest as they need to spend electricity in order to mine new blocks.
Pretty good answers! 
In bitcoin, the difficulty target is being adjusted every 2016 blocks. (Approximately every 2 weeks.)
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It is important to make sure that miners spend money (on electricity) while mining because they need to be incentivised to earn back rewards and transaction fees to cover losses. (Play by the rules if they donât they lose money)
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It would be extremely difficult for someone to go back and change a previously added block because then you would have to rehash every block and mine meanwhile new blocks are continuously being made making the task even harder.
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The network regulates mining difficulty simply by the number of miners currently active. More miners lower target number but higher difficulty (because there is a larger area or probabilty of failing to guess the number) and less miners high target number but lower difficulty. Also trying to keep to the 10 minute block interval creation.
Not the whole chain. If we alter a block that is 100 blocks old, we would only need to remine those 100 blocks. Thatâs why older blocks are considered more safe than the newer ones.
The incentive is the block reward. Its important for the security of the network. The only way to add new blocks is to spend electricity, which means that the blocks are backed up by real energy. We made something digital be backed up by something real.
- Because if they are shady block producer they will be punished with electricity money.
- Because the hash of the block would change creating a domino effect on all other blocks connected so forth in the blockchain. Being rejected you would have to remine all other blocks and at the same time overmine all other miners actively mining new blocks per 10 min.
- By lowering the hash target aka block nonce
- Why is it important to make sure that miners spend money (on electricity) while mining?
When Miners spend money in electricity they are incentivized to follow the rules - Why would it be very difficult for someone to go back change a previously added block?
They would have to edit every single link processed before as well as the upcoming blocks - How does the network regulate mining difficulty?
by hitting a specific low target in order to add the nonce
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While this is true, there is something which is even more important. The only way to add new blocks is to spend electricity, which means that the blocks are backed up by real energy. We made something digital be backed up by something real. This is why the electricity matters. It makes sure that there has been a significant work behind each and every block in the blockchain. This makes the network very secure and immutable.
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It wouldnât take thousand of years. Changing an information in the newer blocks is easier and possible. While this is still hard to do in bitcoin (not impossible), many other network have attacked in this way. In order to successfully change the block in the past, a single node needs to have a mining power higher than 51%. This is known as a 51% attack. You will learn this later on in the academy.
- While this is true, there is something which is even more important. The only way to add new blocks is to spend electricity, which means that the blocks are backed up by real energy. We made something digital be backed up by something real. This is why the electricity matters. It makes sure that there has been a significant work behind each and every block in the blockchain. This makes the network very secure and immutable.
1. Why is it important to make sure that miners spend money (on electricity) while mining?
The reason the miners must spend more money and energy is; the target must be lower than the previous hash, and the lower the target the higher the difficulty.
2. Why would it be very difficult for someone to go back change a previously added block?
Since the block header includes the hash of the previous block. So if you want to modify a transaction, in one block, you will need to also remine all of the blocks following the block, which contains the transaction you modified. Because following blocks gets longer and longer, it requires an extensive money, time and energy to remine. That is why nearly impossible someone to come on this idea, unless one has 51% of the hash rate.
3. How does the network regulate mining difficulty?
The more the miners are in network: the higher the difficulty and the lower the target No.will be.
It would take an attacker forever to change something in the past is they have less than 51% of the hashing power. However if an attacker can achieve more than 51% of the hash power they can attack the network successfully and change some of the blocks in the past. (Easier to changed the new ones, and way harder to change the older ones) This is known as the 51% attack and while its not likely in bitcoin, it has been done on the smaller networks such as ETC. (Ethereum Classic) You will learn more about this later on in the academy.
Because the miners need to be incentivised to mine correctly and keep the blockchain impeccable without mistakes lowering the risk of losing their stake.
As any alteration will alter the hash output of that block, altering hash output of the next block which would have to be changed in all the subsequent blocks.
The more miners mining causes the difficulty to become greater and the nonce will be lower therefore the chances of guessing that number become less.
It also makes the network very secure and immutable, as the only way to change the past is to spend the large amount of electricity again. Each block in the past has a real world energy connected to it. 
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Great answers, especially the second one!
I wouldnât say practically impossible but rather very hard. We have seen smaller networks getting attacked with the 51% of the hash power. As far as I know, bitcoin is still standing strong. 
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Thanks for helping others. 