How do I remove white residue on bathroom floor tiling?
That does not look like residue.
1.) if you get it wet, does it fade or change in color?
2.) if you scrape at one spot wiht your fingernail, does it come up?

Looking at the photos you've posted, I think that is both mold (in a few areas - showing that the area does indeed stay wet often as you imply), and damaged flooring.

I suspect the material of that flooring is porous and the water has actually damaged the "cheap" surface.

Also, it looks like you may have used a scrub tool on it, which has scored the surface further (the scratches and lines), and the condition will continue to get worse.

My recommendation at this point is to keep it clean and dry, solve the issue that introduces the water/dampness. you will have to replace the damaged areas to return it to like new condition.

If that is real wood, and it has a finished surface, you can probably use a buffer on it, but it does not look like real wood.