Can you use chalk paint to paint over moulding that has been stained?

yes

Yes. I always stain things before I chalk paint them. Gives them more of a shabby, distressed look.

Yes but you might want to lightly sand first and use a primer paint before you apply chalk paint

Always put a primer over any stained material, unless you want it to bleed through for a distressed look.

In one word "yes" you can, however, like Sharon (from Florence, Oregon), I'd recommend a primer just in case any stain "bleeds" through the layer(s) of chalk paint. You will probably require two coats of chalk paint and, as I found from personal experience, make sure you stir the chalk paint very well before applying each coat.

Milk paint works better in my opinion. etches in great. did it in my old mobile home with those horrible paper covered cabinets.

also you use a color similar to what you are going to repaint.. no scratch through.

Yes you can, but first sand and prime. Seems like chalk paint is The go to these days but regular semi- gloss or satin paint from Home Depot or other paint store will hold up better, be more washable and I'm sure you will be more satisfied in the long run.

Yes, but you can't go back again. If you use a good primer between the stain and the chalk paint, you might be able to sand the chalk paint off if you change your mind next year. But probably not, so you would need new molding. The same, actually, for any paint treatment over stain. Best wishes 😇