The dark oily stains would concern me. They sound like pet urine stains. Has anyone had pets there?
If they are pet stains, the wood is perminately stained all the way through. The only solution is replace the wood. The stains cannot be sanded or bleached out.
Or, the stains may be from water/drink spills. If so, the staining is just on the top finish sanding and refinishing will remove most of them.
The loose tiles may not be a problem. Or at least should be repairable. Is the entire square loose, or are sections of wood within a tile loose?
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