Multiple FAQ pages using FAQ module
Yes, the FAQ module provides the ability to have separate categories of FAQ via the taxonomy module as per the project page:


  "In addition, if the 'Taxonomy' module is enabled, it is possible to
  put the questions into different categories when editing. Users will
  need the 'view faq page' permission to view the built-in 'faq' page
  and will need the 'administer faq' permission to configure the layout,
  etc."


To use the individual faq categories, use the urls: faq-page/[tid] - where the [tid] is the term ID of the category you want.

You can also use views to make additional faq pages for specific categories if you like.