Hi,
The search should be okay – but the category filtering on the category page might be a problem here. See you try to filter the items in the “Faq” category page to switch to a different category from the same taxonomy. But because this is a specific taxonomy term (Faq) archive page, it’s not possible to simply change it to another one, as that is a different archive alltogether. An archive page for a category should always display items matching that category – because that is what it’s made for.
This could very likely work on the post type archive page though – so showing everything from that post type then filtering by taxonomy or vice versa.
Another possibility is to not use the archive for that, but simply use the plugin on a separate single page, preset the filter to the “Faq” item, then enable the auto populate. That way it will automatically show the items for that FAQ in the search results container, and the user can switch to a different categor – like this example.