Thank you so much for your answer!
Yes SEO seems to be an issue, since the content will be duplicated - could even lead to a google-ban.
but it is my understanding that WordPress, itself, can only run in one selected language at a time
I thought this too, but just 5 Minutes ago i've read about 'WPLANG' which is defined in the wp-config.php. This may look constant, but it seems that you can also set it up, that it changes for every individual user using sessions.
Source:http://code.tutsplus.com/articles/new-wp-config-tweaks-you-probably-dont-know--wp-35396 => Nr. 6
I will try this out tomorrow, but first i have to translate my theme and some plugins.