Why is it important to make sure that miners spend money (on electricity) while mining?
Money spend for electricity basically represents the effort of mining. If the effort of mining would be close to zero, so very easy, than previous blocks could be changed and reminded which would then result in the loss of security and immutuability (see question 2).
Why would it be very difficult for someone to go back change a previously added block?
By changing just a single bit in any data of ablock, this results in a completely changed hash of that entire block. As the hash of a block is created by using the hash of the data, the nonce and the hash of the previous block, any changed hash of one block would affact all hashes of following blocks. Consequently one would need to mine all blocks following the block with changed data. To do this with a single computer or mining farm and be faster than entire mining network is far from being realistic. One would need to be faster than the network because always the longest chain wins and is accepted from the network. Whoever would theoretically have this astronomical hash power, could earn much better doing legal honest mining.
How does the network regulate mining difficulty?
The difficulty level is adjusted to maintain a constant block mining rate of approximately a new block being mined every ten minutes. Mining is basically trying different inputs via brute-force method for a has function until by chance the output number is smaller than the currently requested difficulty target. A higher difficulty means that the hash needs to be smaller than a lower requested number and consequently the avergae time of guessing takes longer as the probability is lower.