Hi Mario,
Thank you very much for your kind words!
I have looked at the front page on a mobile view, but I can’t see any default search bar there at the moment, so I am not sure where should it go or what should be replaced.
Divi has a lot of different layouts, I believe it should let you change the header in mobile view as well. I do not recommend changing their theme files, unless you are using a child theme and you know what files to change. Divi is super versatile, and I don’t know how good of an idea is to make changes in their files.