Sorry to see this, Urs!
I cannot recreate these issues, so here is what I would recommend doing:
1. Activate a default theme like Twenty Twelve or Twenty Seventeen on your site. When one of these themes is activated, do you have the same issue with the double content?
2. If so, then proceed with the complete set of troubleshooting steps on this page → https://theeventscalendar.com/knowledgebase/testing-for-conflicts/ After EACH STEP in that process, check back on your issues and see if anything improves along the way.
Let us know what you find! 😀
Thanks,
George