Thank you very much for the information and your time. We located the problem in the theme, so it is solved.
No, not exactly. The first bit is true, but I did not delete the “events” post type as a whole. I deleted only one single post of this post type (and for test purposes two more). The other events-posts are still in use and my problem is, that these deleted single posts are stil showing up in the previously described places.
So I suspect they are despite that still in the database like you described in the next paragraph.
Thanks for looking into the matter and I hope you can help me further.