I uploaded a new version (v1.1) of the game here. I got rid of filenames with umlauts (hopefully I got them all), and built the game using a version of Unity that does not have the duplicate input bug. Issue 2 might still be present (i.e. the game is probably not marked as an executable) but I can look further into it once the other issues have been solved. If you are still interested in trying the game out, let me know if there are still issues.
Again, thanks for the feedback!