Proof-Of-Work Algorithm explained by a newbie

You don’t know me, but if you have gone over any of my recently posted articles telling my struggle as a crypto newbie, you surely know that I have this necessity of wanting to understand everything, same as you or at least that is what I hope.
So, I did my best to understand what a blockchain is and I wrote my impressions on it but I needed more information to understand how they work and how I was going to get rewarded by mining Webchain . I repeated it several times and I made you believe I understood what it meant to invest Processing Power to mine coins, but I couldn’t explain it to my mom (who is a physician) so she could understand and that meant I did not fully understand that working methodology either.
I found out that in terms of blockchains, a Proof-Of-Work (PoW) algorithm is used to confirm transactions and produce new blocks to the chain. With PoW, miners compete against each other to complete transactions on the network and get rewarded.
So, considering that mining is a process where your CPU (in case of CPU only mining cryptocurrencies) becomes a sort of special network node (a miner) and takes the responsibility of solving a mathematical puzzle by investing processing power, the rules of this process are set by an algorithm and that algorithm is called Proof-Of-Work. Another interesting concept I came into was “hash”, in mining that is the term that the solution to the puzzle is given. When a miner submits a hash to solve the puzzle, the Proof of Work algorithm allows each other miner in the network to verify the hash (this is called peer to peer protocol) and if the solution is correct allows the generation of a new block, then the old transactions are placed in this block and the process starts over, this is what keeps the blockchain growing and growing and it is also the reason why blockchains need no centralize authorities.
After grasping this idea, I started wondering how the algorithm manages it to assign the complexity of each mathematical puzzle, as I imagined it was also part of its functions. It goes something like this:
If blocks are quickly added to the blockchain, the network gets cancer. Our organism usually has the right number of each type of cell because cells themselves send signals to control how much and how often they need to be divided. If any of these signals are faulty or missing, cells may start to grow and multiply too much and form a lump called a tumour. Just like that, it happens with the blockchain, if you look at each miner as a cell, what the PoW algorithm does is to control the adaptability of these within the network. Adding one miner adds more processing power to the blockchain and therefore blocks will be generated more rapidly and that is the cancer of blockchains because blocks are not endless.
Wrapping up, how complex a puzzle is depends on the number of users as it controls the current power and the network load. The solution needs to be according to this parameters as well, if it is too easy to be found you get spammers and attackers which will kill any possible market capitalization for the coin, and if it is too hard not all nodes will be capable of analyzing if the calculations are correct in time.
Just as a reminder for us (and for my mom) I will list the functions of the Proof of Work algorithm:
-Regulate how complex the mathematical puzzle to be solved will be
-Let senders (miners) submit a hash (the solution) to solve the puzzle
-Thanks to the Peer-to-Peer protocol, the algorithm allows each miner in the network to verify the each other’s hash
-If the solution is correct, a new block is generated
-It places the transactions on the new block and starts the process over.