First, please note that you should log a new issue as a separate ticket – please read terms of service.
How can I change the order of visualization of the sections?
If you mean the homepage sections display, please control this via Appearance → Customize → Theme Options → Layout.
If you want to reorder the Jetpack Food Menu sections, please do this in Food Menus in your WordPress admin.
On the auto-generated horizontal menu there is a repeated item: what problem could be?
Please check out your Food Menu organization in Food Menus and Food Menus → Menu Sections in your WordPress admin.
Lastly, I would like to remove the button that appears after the menu (the orange “Menù” in the attached screenshot).
Please try using your web browser code inspector to determine the CSS styles you need to apply to modify the theme. Here is custom CSS hiding the button: