Hi!
Thank you for updating and the details, it helps me a lot.
1. In this case, you need to turn off this option here: https://i.imgur.com/C0LuL76.png
It will exclude items that are not assigned to any categories.
2. That is not possible, the files need to be uploaded via the media library, so they are registered within the database.
3. There is a way to index the PDF file contents, you can find all the details in this documentation section: Searching file contents
The parser scripts should be able to exctract these metadata as well as the content from the PDF files. If the PDFs are not secured, encrypted or protected, it should very likely work. Making exclusions based on this metadata is however not possible.