Hi Stuart,
thanks a lot for getting back to me and helping me finding a solution. I really appreciate! In the meanwhile I also had the idea to find the error in the theme I am using or in one of the plugins.
As you suggested I also tried deactivating all plugins and the reactivate one by one. So I found out that a plugin for the Checkout Form is causing the problem.
I could find a workaround and now it is working fine!
Thank you again!