1. I the texts there was said that it would take a long time to download the blockchain the first time, more than six hours. Despite using a lame old hardware with a really crappy Internet-connection, the download stopped after about half an hour with 67714 blocks. Can this be right? What ist the number which should stand there?
There are currently ~286000 blocks. Regardless of your connection or your machine, this will take a few days to download as the Bitcoin protocol isn't made for efficient distribution of large amounts of data. There's a bootstrap torrent you can find on this forum to download a large part of the blockchain using bittorrent, which should be a lot faster.
Alternatively, there are light clients such as Multibit that don't need to download the entire blockchain. They are ready-to-use much much faster.
2. After starting bitcoind from the texts I read, I would suspect that the next step is to create me a wallet. But when I look at the commands bitcoind is accepting, something like "create-wallet" is not to be found. With what command can I create a new wallet?
A wallet is automatically created upon first startup.
3. In the FAQ I found that there are small fees to the transactions. That sounded plausible. My question ist: Who is deciding to whome this fee will go? Or, to make the question a bit more provocative: What do I have to do to make the fees from other transaction go to me?
The fee goes to the miners that add new blocks to the blockchain. The FAQ will have more info on mining.
