Ok, thank you very much, I got it now.
But why do we need tx fees if the miners will get the block reward? Isn't this enough?
There is a limited amount of space in a block. The miner needs to decide which transactions to include in the block. The transaction fee is a way for the transaction sender to provide an incentive for the miner to choose the transaction. You don't have to provide a fee if you don't want to, but since the miner is profit motivated, they will choose the transactions that DO provide a fee unless they have extra space or they feel very charitable.
Is this process designed for the time when all blocks are found
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And btw - how are transactions transfered once all blocks are found?
There is no such thing as "all blocks found". As long as bitcoin exists, there will continue to be more blocks.
or the block reward is so small that miners won't work anymore because their reward is too low?
The fees will slowly replace the subsidy as the main source of revenue for the miners. Approximately every 4 years (exactly every 210,000 blocks) the subsidy is cut in half. Eventually the subsidy will be less than the fees. Then (in about 110 more years) the subsidy will disappear completely, but mining (block building and solving) will continue to earn the fees.
How much is the tx fee reward per block approximately?
That depends on how much the transaction senders are willing to pay. It changes with time. For example, the average fees in the most recent 5 blocks is 0.39829937 BTC per block, while the average fees in 5 blocks chosen randomly from December 25 (blocks 501000 through 501004) was 6.30986372 BTC per block.
So how much tx fee is added to the subsidy?
The transaction senders choose how much fee they want to include. The miner then chooses the fees that pay the highest fee per byte (or block weight) until the block is full. If people are paying higher fees, then the miner gets more revenue.
Just to get an idea if it's just 0,0001 BTC or more like 1 BTC per Block in total of all tx fees?
As bitcoin becomes more popular, there are more transactions. As there are more transactions, the senders offer higher fees to get their transactions confirmed. This increases fees overall. If the fees get too expensive, then people stop using bitcoin. The reduction in use means less transactions which means it is easier to get a transaction into a block. Therefore, people pay less fees. Eventually the fees get cheap enough that more people are willing to pay them. This increases the number of transactions. It is likely that the fees and transaction volume will bounce around a bit until it reaches some equilibrium. It is not currently known where that equilibrium will be. The people will decide for themselves as the system develops and matures. I expect that the total fees will be higher a few years from now than they are right now.