In which moment would the miner recollect the fees? on putting the transaction on the block, or when he broadcasts a succesful block to the network? Would this be a new transaction on top of each tx, how do the miners exactly recollect the fee?
The transaction fees are added to the block reward and paid to the miner's mining address as a part of the coinbase transaction in a block. This means that all block rewards are "tainted" with whatever fees are accepted by the miner (which can of course be zero fees, i.e. zero tainting).