How do you detect "spam TX" that are just put in the block by the miners to reach the maximum amount possible, e.g. send coins from miner A to miner A's 2nd (3rd...) address?
Why would a miner do that when there is nothing to be gained from it? There are plenty of natural transactions to process for fees?
How do you detect whether a miner is actualy creating only a single hash and thus relying on luck or secretly creates many hashes in order to have a higher chance to win?
Only one hash would be allowed from every node so, you'd need a separate node for every hash you want to play. If the network uses IP addresses to distinguish nodes, how many IP addresses do you think it would take to increase your odds of winning when the odds of winning are 2
256-1 to 1?
Answer: 1000x more than exist.
But I have my custom wallet, that does what I want. How do you make sure that my cheating attemt is detected by the network?
This has already been addressed by other parts of the Bitcoin protocol. It has nothing to do with the change to the mining process I'm proposing here.
For now you have not even explained how you want to make sure your system is not cheated.
You haven't yet explained how you're planning to cheat it.
Its more expensive to set up several million nodes than it is to calculate the same amount of hashes.
That's good, it discourages this behavior. The potential return from winnings doesn't justify the investment.
How do you make the distinction between 1st and 57845784th hash?
Math.