Is your locale set to de_DE? The module should include a /lang/de_DE.php
There's a lot you can do to customize your date display. By default, the calendar will fall back on your lang file to get the date display format for your locale. If you want to customize it, you can specify an override in the $customDateDisplay array that comes with event_calendar/_config.php.
I know it's a huge thread, but we developed this recently in the Preview: Event Calendar Module thread. You may have to go back several pages. I worked with a German user, Banal, to develop the localization. That's the best source of documentation we have for it right now, unfortunately. I hope to get it into the wiki soon. If you're having trouble with it, just paste your code and I can help you out.