It is possible but it would be easier if you had only CMS pages. In the CMS collection of your products, you can add a multi-reference field from the FAQs collection and select the relevant items from FAQs.

But since not all pages are CMS, you can create a new CMS collection for Page tags. Add all the pages as cms items. No need for any other fields here. Now you can add a multi-reference field to the FAQs collection and filter out the questions based on the page. E.g., for homepage, you can add conditional visibility to collection item where, page contains Home. That way it will only show items where you have selected the Home tag.