Smudger,
After looking at photos,
There is a considerable amount of grout on slabs, this will affect the finish.
These areas are liable to be visable on the finished product.
I would first remove grout residue on slabs with a good grout cleaner
we use ltp ( Grimex). With slow speed scrubber with polyproplene brush,
After completing this procedure, completely clean area and leave to dry naturally.
Then apply ltp stone oil. Or similar products stated in earlier posts.
Andy