That was not it, but I think I solved it.
Because of your comment, I've tried other functions (as those would be broken by proxy problems too) - like changing my username - and in Opera (interestingly not in Firefox) the error "Security Token did not match. Possible CSRF attack" appeared.
I looked it up and its often connected to cookie problems. So I've added this line to the .htaccess
php_flag session.use_cookies on
That did it.
Thank you very much for your help.