I am considering using style 2 in header. And when choosing that the search moves with the menu down in style 2. I want it to stay in the top of the pages as in style 1. I am using style 1 at the moment.
The feature you mentioned requires a lot of code customization and can’t be covered from this forum. You can choose from the available two options or if you really want this feature, you can contact our customization team.