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). 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?
yes
So every adress contains 2^96 public keys and also 2^96 private keys?
Doesn't this reduce the difficulty to bruteforce an adress?
2^160 is such an insanely big number that it's not an issue.