I think I would like to know WHO exactly gets the transaction fee?
I mean, If A sends 1 BTC from her wallet to B and it arrives into his wallet, then who gets a transaction fee.
Isn't this the point of a P2P system?
I understand if you use some 3rd party to do the transfers, as they want to make money, in fact it will be their main way of making money.
In my scenario, is there a fee and who gets it?
K
As to the question of "is there a fee?", that is entirely up to the sender of the transaction. Fees are mostly voluntary in bitcoin. There are a few conditions where most (though not all) of the wallets in widespread use enforce a fee on the sender of the transaction, but as long as the transaction is less than 10 kilobytes in size and all outputs are greater than 0.01 BTC the sender can choose to use a wallet that does not force them to include a transaction fee if they wish.
As for who gets the transaction fees, they go to those who are doing the work of maintaining the transaction ledger (the blockchain) that everyone uses to validate the history of the transactions that they are sending and receiving. These would be the peers that are commonly called "miners". They supply the proof-of-work that makes it nearly impossible to double-spend bitcoins. Without their work, bitcoin couldn't exist as a viable currency or payment network. So while bitcoin is "peer-to-peer", it requires more than just a "sending" peer and a "receiving" peer. There are peers that are relaying the transaction, and there are peers that are "confirming" transactions into the blockchain.