Thank you everybody for your help clarifying what's going on.
Still, there's something unexplained.
How can a merchant even ISSUE two times a spending of the same bitcoins?
How can this happen in an "automated" way, because I suppose I can't double spend my bitcoins from my bitcoin wallet, right? So it must be something coded somewhere, right?
And if this is coded, how to trust the issuer of those bitcoins again?
Oh, scary! When buying with bitcoins in a shop for example, then it's too long time to have to wait 10 minutes for the transaction to be completed. Doesn't this mean that people could use hacked wallets that double spend all the time?
websites such as overstock. take days to deliver goods. so its easy for them to wait for confirmations. but as for the "starbuck's" scenario of waiting 10minutes + for payment before they even pour the coffee into a cup. that is simple to get around
PRE-PAY (research: officially called offchain transactions)
imagine starbucks had their own online wallet service you register and deposit lets say a weeks worth bitcoins for coffee and cookies. and thats confirmed on the blockchain. and starbucks 'credits your account with that X btc
now when you physically walk into starbucks you pay using the starbucks wallet and pay through the wallet. the starbucks wallet is nothing more then a sql database balance to show how much people have pre-paid.
that way starbucks know they are getting paid, because technically they have already been paid. the customer is just agreeing to drop his balance by X amount on the stabuck sql database (offchain).
I agree that Bitcoin times are too long for everyday shopping.
But I think this will be replaced by some web wallet service, there are already many and it's easier to rent some service like this than to build own infrastructure, I think.