Your tile must be marble, because the same thing happened to me before and after i dropped some wax on my marble tile, i could not remove the wax at all, its like the wax got etched into the marble tile, hmm
I too have some mold in my room area and the HCL89 product from http://hcl89.byethost10.com looks rather promising and i also intend to use it as i feel that the mold in my room area is spreading
This is definately a good idea, because sunlight will always prevent moisture from over gathering in a certain area but thing is most of us work during the day so we don't really open our windows more than we should to prevent over moisture