[E. von Hoegh]

you see, the trouble with common sense is that it isn't all that common, but the op question is a good one and not so easy to answer. i tend to believe that a good filter cannot hurt and may help to improve the optical performance of an otherwise mediocre system. it is worth a test, and we'll see.

Possibly. A monochrome filter will help out a lens with chromatic aberrations.

But - putting a multicoated filter on a single coated (or uncoated) lens will not make it perform like a multicoated lens. It can't, if you think it through. There are all of the un- or single coated surfaces there in and on the lens, reflecting precisely as they always do. A far more effective approach would be to use a proper lens shade, which will make a huge difference in how an uncoated lens performs.