You can clean it with alkaline or acid or both,start with alkaline cleaner,if you need more umph,go with a restorer,as far as sealers go,I would just use a good impregnator.
Larry,slate is so porous I dont know how long it will take to get all that out,so I would say do a test area w/stripper and see how difficult it will be to remove and then price it from there.75-1.50 to clean .50-to 1.00 to seal.
(per sq ft)