Hello Uli,
Thanks for updating in! As I have mentioned earlier, your form is using <table> HTML element which is not really responsive enough. If you can recreate the form using 3rd party form plugin like Gravity Form or WP Form plugin because it will allow you to create a from with a responsive design in mind.
Even if we add custom CSS code to your current registration form, sooner or later, conflicts or issues will appear. Other browsers might still not be able to display it responsive because again it is using <table> HTML tag.
Be advised that custom CSS coding is beyond the scope of our support under our Support Policy. I
In the meantime, if you got this registration form from a 3rd party site or from a coder, please contact them instead and ask for further assistance. They should be able to assist you on how to make it responsive.
Thank you for your understanding.