Hi Andreas,
Thank you very much for the details!
I tried to log-in to your site back-end to check the configuration, but I am getting this error: https://i.imgur.com/PABEdNa.png
Also, can you please ask the theme developer which files contains the search bar you need to replace? Please note that custom coding/implementing is not part of our support, so I cannot guarantee anything, but I will try of course.
