basically, what you are trying to create is what is called a Master / Details page set.
the library page is the Master page that shows all the FAQ categories, and the library_results.php page shows the details of the FAQs for the selected categories.
In the database starter kit tutorial:
I give steps for creating a creating a very similar master detail page set for Categories and products that belong to the selected category. If you follow that tutorial, it should help you understand how the recordsets for your page should be created.