So who then receives the transaction fee?
Thank you.

You make a transaction, add a fee. Naturally, the transaction will be added to a block that will eventually be processed by a miner (pool, solo, doesn't matter). The fee bumps the priority of your transaction data, pushing your transaction at the top of the queue (admitting there are only fee-less transaction waiting in the queue). Whichever miner that revolves the block holding your transaction in will receive the fee.

Not exactly. The miner will confirm the transaction and receive the transaction fee at the same time. The miner has to be online in order to mine. A miner that is offline won't be mining, and won't receive the transaction fee.

The act of the "network" confirming the transaction is actually the act of a single miner finding a block.  A "block" is really just the confirmation of the transactions contained inside.  Thus, if you as a normal user include a transaction fee in your payment to Random Service A, in approximately ten minutes or less, some other online hard-working miner will confirm that transaction in the block he/she solves.  That person will receive the transaction fee that you paid, and Random Service A will receive the remainder of the balance you sent.

You are correct in that including a fee does improve your chances that your transaction will be included in the next block.  This is because it is entirely up the miner itself whether or not to accept transactions that don't include a fee.  At the current moment, I'd say that most miners (and pools) are willing to accept any transactions regardless of whether there's a fee or not, though already we are starting to see some very minor delays.  In the future, it is expected that because the reward-per-block diminishes over time, that eventually it will be the transaction fees that will motivate miners to continue mining, rather than the actual reward. 

No, I don't think that's what Richochet said, and I think Ricochet's explanation (and your previous understanding) is correct.

Payment - the 50 BTC and any transaction fees - only goes to the miner who solves the difficult problem.

If you continue mining you might generate a block (solve a difficult problem). If you do, you'll receive 50 BTC. You may also receive a transaction fee. You won't receive any transaction fees unless you generate a block.

You will only generate a block if you are online and mining.

Originally there was a strong motivation to have mining enabled, as the cpu requirements to generate a block (and thus win the 50BTC+fees bounty) were minimal. These days, there's SO many computers out there mining (and using custom mining tools that use the GPU instead of CPU which is far more efficient) that on my 3-year-old PC the average time between block generations using the native client is some 1500 days! Even with a GPU miner it worked out to be 1 block every 120 days.

If you've got a reasonably new PC, run a GPU miner and connect to a mining pool, you may find that you can mine a few hundred coins per year in the background and that's certainly worth it to enough people that some of the mining pools out there are doing over 100Ghps. By comparison my GPU was doing 27mhps, and my cpu was doing 4!

The question is not about making money, the question is about maintaining the network, basing entire network only on miners is bad because real serverless p2p networks are better with more permanently online members, so that the network will be more resistible to attacks.

I'll say it again, some people who mine do so because their conditions negate the effects of consuming electricity.  Most are people who live in small efficency apartments heated only by electro-resistive heating, and have neither the room nor the resources to set up a rack of machines, but do have a decent gaming class video card.  Some people live in areas with below average costs of electricity, and have a comparative advantage as a result.  By definition, roughly half of the bitcoin network exists in places with below average electric costs, but some can be very low.

Not sure if I read it right but say someone wanted to send another person 20 BTC. If transaction fees occur where does it come from. Would the person get 19.99 BTC or would 20.01 BTC come from the senders account?