Recycled fuel leaves only fission products that decay to below background radiation levels in a few centuries, not hundreds of thousands of years.
Yes, one can measure and calculate precisely the composition of fuel that comes out of a reactor. I suggest you read the book "Plentiful Energy" by Till & Chang to find out more, including a detailed description of the pyro processing constituents (chemical composition and radioisotope mix)
If you want a broader overview, maybe watch this video I did recently in Canberra at the National Library - I'm the panelist on the far right:
http://bravenewclimate.com/2014/08/0...a-has-to-have/