Ok, thank you, I'm still a bit confused.
When I make a brainwallet on brainwallet.org I can type every passphrase I want, no matter how long it is (I tried it with one of my texts, ~6,000 signs).
Correct. Brainwallets are a very bad idea. Any brainwallet that you can think of, can be thought of by someone else. This will result in you losing your bitcoins.
Ok, this is not a private key, but am I right that there is an infinite number of passphrases like this which fit to every address?
Sure. There are an infinite number of phrases that will hash (with SHA-256) to each private key. Therefore, there are an infinite number of phrases for each address.
So every address contains 2^96 public keys and also 2^96 private keys?
On average.
Some addresses may have additional private keys, some may have less. As far as I'm aware, it has not yet been proven whether or not the results of RIPEMD-160 and SHA-256 are evenly distributed.
Doesn't this reduce the difficulty to bruteforce an adress?
Yes. It reduces the address space from 2
256 to 2
160.
In other words, it reduces it from a really, really, really big number, to a really, really, really big number that isn't quite as big.