What categories/classes is a Ground Instructor able to instruct on? Under §61.215 Ground instructor privileges, it says 


  (a) A person who holds a basic ground instructor rating is authorized
  to provide—
  
  (1) Ground training in the aeronautical knowledge areas required for
  the issuance of a sport pilot certificate, recreational pilot
  certificate, private pilot certificate, or associated ratings under
  this part;
  
  (2) Ground training required for a sport pilot, recreational pilot,
  and private pilot flight review; and
  
  (3) A recommendation for a knowledge test required for the issuance of
  a sport pilot certificate, recreational pilot certificate, or private
  pilot certificate under this part.


But it doesn't say anything about what kind of category and class the ground instructor may instruct on. Is a separate GI rating required for each category and class? or is there one GI rating that covers all categories and classes?
The basic ground instructor covers everything you quote.  The only additional privileges you can get are those granted by the advanced ground instructor rating.  My ground instructor certificate just says "Ground instructor" on the front and "advanced instrument" on the back.  No other ratings or limitations.

Things like reading charts, familiarity with regulations, weather information, fundamentals of flight and other required knowledge topics do not depend on category or class of aircraft.  You just need the BGI (and IGI for instrument) to teach ground and endorse written tests regardless of the aircraft the student is or will eventually train in.

The only other benefit to having a ground instructor certificate is that it is required to get a gold seal on your CFI certificate.