Hi there,
Does the search issue is now fixed? That’s because the header and banner are now displaying upon search.
About that rating issue with no header and footer, it’s because header and footer are needed to be assigned to existing pages, and they page with identities.
Those rating pages are recognized as archive pages, and you can’t assign header and footer to archive pages, yet, unless they are set to global. You can verify that by viewing the source code in the browser <body class="archive post-type-archive ... >
What you need is to convert those pages into custom post type with custom permalinks. But I doubt it can be done easily since your vendor code is made that way (archives). You may want to consult it to a developer for further enhancement as I’m not really sure how their plugins works.
Example, the /store/havasu-store/
This is an archive page which is just okay, /store/{TERM NAME}/
, this tells the Wordpress system that it’s an archive page with a term-name as identity. That’s how rewrites and permalinks works, but when it comes to this, store/havasu-store/ratings/
, the format will be like this, /store/{TERM NAME}/{UNKNOWN SLUG}/
, it becomes a new identity which Wordpress can’t understand (/ratings/
is never part of Wordpress permalink/rewrite system), so in the end, it became an archive page. A bit complex 
Thanks.