Good evening Gunnar and welcome to the Events Calendar Support forum!
Thank you for reaching out to us.
I would love to help you with this topic.
My first, pretty hackish, approach was creating Custom Fields and rearrange them in all forms/views. But a custom Image Field is not given and I don’t know (yet) how to get the Custom Field in templates. So the Custom Field mechanics don’t really satisfy my needs.
You did not specify, but I believe that you tried using the pro additional fields option to accomplish your initial approach: https://theeventscalendar.com/knowledgebase/pro-additional-fields/
Since there is no “Upload image” field available there, I think you might be a prime candidate for using the following third-party plugin instead: https://wordpress.org/plugins/advanced-custom-fields/
As for rearranging the fields, the best and most update-proof approach would be to create a template customization.
You might want to read our Themer’s guide to get a sense of how that works.
Let me know if that helps.
Have a great day!
Geoff B.