Could someone write or draw a complete explanation how the currency exchange feature works. Lets say Alice is newcomer to ripple but she has yen bills in her pocket and wants to buy a computer from a webshop that wants to see no other currency than USD but has previously done business with a ripple gateway.
Alice deposits the Yen bills at a gateway and the gateway issues here a Yen balance in the Ripple system. The webshop selects a USD gateway and configures its Ripple account to accept USD at that gateway. When Alice goes to buy, the Ripple network does pathfinding and matchmaking to find a way to exchange her Yen balance at her gateway for a USD balance at the webshop's gateway. Assuming both gateways are issuing balances that are liquid, a low-cost path should be found and the exchange takes place. Now, Alice's gateway owes her less, the webshop's gateway owes it more, and the webshop considers Alice to have paid them.
The wiki does not clearly explain what are all the places that have any significance where XRP is used and for what? I heard from someplace that it funds all OpenCoin functions generously, but wiki says OpenCoin only gives them away for free and the only place they are ever used in the whole system is for silly small transaction costs. Somehow I don't think I understand.
I'm not sure what you don't understand.
The same for various IOUs? Does the distributed ledger track all various IOUs or only XRPs? What is a role of user-IOUs? Do such things exist in the system?
An "IOU" is just a negative balance between two users in some currency. The ledger tracks balances between pairs of users.
What happens to the external currencies? Where does the yen bill end up to? Where do the dollar bills to the merchant come from?
The gateways hold them. The Yen bill winds up at the gateway and as a result of the transaction, it's now owed by the gateway to whoever provided whatever Alice traded for her Yen balance. The dollar comes from created the offer of dollars that Alice accepted.
How does the gateway business operate in typical moneyflow? I mean what is the typical business of how a gateway connected to a very big merchant operate? How does some gateway that refuses to serve any merchants and only accepts ordinary people that typically want to deposit their paycheck in dollars to buy stuff from some outside rippleshop operate as money-flow in all different kinds of currencies/IOUs that a gateway should handle? For simplicity you could assume only one type of fiat money accepted per each gateway.
A gateway makes a public offer to redeem its Ripple balances for currency. A gateway makes a public offer to accept currencies and issue Ripple balances. So long as the gateway is considered reliable, its balances will be generally valued at very close to face value because you can easily either redeem them for face value or trade them to someone else who can. You deposit currency at a Ripple gateway and can then trade balances with that gateway on the Ripple network as if they were the currency (or something very close to it).
What exchange rates are used in each step? What mechanism sets them and where?
Ripple supports exchanges between any two asset pairs. An asset can be XRP or it can be a currency and an issuer (the issuer can be, but doesn't have to be, a gateway). The rates are set by supply and demand and anyone can place or take offers from the exchange order books. A payment can also draw from multiple exchanges to get better rates.
Where and by whom is what XRP is worth in dollars determined? How much is an 1USD-BobsGatewayIOU worth in dollars?
Purely supply and demand.
Where do the gateways get their profit or cover their expenses fulfilling the promise on the first sentence of ripple.com that there are no fees.
There are no *Ripple* fees (other than transaction fees and reserves). Gateways, like everyone and everything else, are free to charge whatever they want for anything they do. A gateway can charge an account creation fee (to create the account at the gateway, not to create a Ripple account), monthly account maintenance fees, deposit fees, withdrawal fees, and so on. They can also charge a "transfer fee" when their balances change hands. Currently, BitStamp (the largest gateway currently) charges an 0.2% transfer fee. Competition may bring this down in the future.
What is the complete list of parties that Alice must trust in this example one transaction? Who are the parties that the webshop needs to trust?
Each party need only trust their own gateway. You never have to trust anyone you haven't chosen to trust. Payments are atomic.