SAP Basis Clarification and preparation of measures for the use of the Security Audit Log - SAP Basis

How does a blockchain build consensus? Once you decide to send a payment to someone, you must use the Private Key to "sign" it (in German: signature). This means nothing other than that you specify another public address to which you want to send the money and confirm this transaction with your own private key. You don't have a central authority to send the information to, you're going to spread the information to all the other Miners around you. The miners then forward this information to other miners, who in turn do the same. This exponential wave of information reaches the entire network of the distributed community within a few milliseconds. Every time a miner receives a transaction, it checks that the transaction is actually correct. It checks which private key has signed, which public address the transaction should go to and whether the sender has enough "coins" for this transaction. What are consensus mechanisms? Any miner that solves a transaction through complex mathematical calculations is rewarded by the sender with a "fee" (transaction fee). How will it be decided which miner will receive the transaction fee? Because only one can get this reward. Also, what happens when you try a double spending by sending one transaction to one miner and then another transaction with the same money to another one millisecond later? These two could not yet exchange and thus information would be different in the network.