It seems that you're using an outdated browser. Some things may not work as they should (or don't work at all).
We suggest you upgrade newer and better browser like: Chrome, Firefox, Internet Explorer or Opera

Is there a possibility, to show which Achievements I have achieved already?
I assume they normaly shown only in GOG Galaxy. But since there is no Linux Version of it, I can't start it. Or I could with wine, but than it wouldn't find my installed games, since it only searchs for Windows-Games.
Or is it possible to copy the Game-State (I mean there are no real Savegames.) to an other (Windows) machine?

I mean it seems that the game keeps track of the achievements. (Thanks to 11Bit Studios for letting debug symbols in the game.) There is just no button to show them. (Or at least I didn't found one.)