My condo's tiles has hole and little crack, any way to paint/fill up the hole?

I just buy a second hand condo. As a tight budget, instead of reinstall the titles, i only plan to clean it:-

1) Chemical to wash or polish the tiles? Can recommend the product name and where can buy it?

2) As we know, in between the tiles, there is cement and normally it is white color. Now, most of it is become dirty which showing black. Any product can cover back? I think this should have, like what the contractor worker doing.