That's not plastic, it is a very thin wood veneer that has been clearcoated. Try a damp microfiber first to remove the dirt and go from there but a mild plastic polish should take care of it followed by a wax.
That seat looks dirty and all the seats could probably use a good scrubbing. I like LeatherMasters to clean, then protect.
The headliner stain could be most anythingbut any good cloth cleaner should work. Make sure you try the cleaner in a place that's not visible to make sure that it doesn't discolor.
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