I’m hoping for advice so I can get the search window to look correct in mobile-sized browser situations. Specifically, I’d like the search window to not cut off the top of the slider. Also, it would be great if it were centered in mobile configuration.
The reason it’s doing that is because you are not using the theme’s main menu navigation. You’re using what I believe is a commercial plugin for the menu. Couple of issues there. One that menu doesn’t seem to be working on smaller width screens and unless that plugin offers a way to include a search there you are limited in what you can do.
If that is the theme’s search functionality, you could try turning it off and try using this plugin (if it works with your commercial menu plugin): http://wordpress.org/plugins/search-box-on-navigation-menu/
To disable the theme’s search there, just go here:
Appearance > Theme Options > Header > iMenu Options > Searchbar > OFF > Save Changes
The only thing we could assist you with is hiding the search box on smaller screens. You can use this CSS to do that.
Since you’re using a commercial plugin for your menu, you might want to seek their support to see if there is a way to add a search field to their menu. We won’t be able to assist you with their plugin, sorry.