The Marazzi Cult Series porcelain stoneware is a very good product, but it is enamelled and therefore can't be polished.
I am perplexed by the dark spots in certain areas that you have described, as to create these the acid would need to be extremely strong and left on there for a very long time. Are you sure the the dark areas are not created by the grout residue still being on the tiles? Before making any drastic decisions, I would contact a cleaning firm specialising in flooring and have an inspection and diagnosis about all of the possibilities to repair your flooring. Also consider that the inspection is normally free.
If the outcome is negative, you will have to think about a claim against those who have done the damage and at the same time begin to evaluate its extent, with the need for possible replacement.