Hi!
Sure, let me help you out.
1. You have two different options, either set priorities individually, or you can even set result group priorities – whichever fits your case better.
2. The results page layout is fully controlled by the theme. It is best to customize it there, as it is a WordPress core feature. There are however ways to get “fake” results pages. One way is by using the results shortcode, another is using an elementor pro widget.
I usually recommend avoiding these custom hacky results pages and customizing the core results page.
3. Yes, you can use it as a menu item. It may need some adjustment, because menus items are usually not designed for interactive elements, but only for regular links.