Hi
They appear to be the shape of lice rather than mites but as you say they are quite dark in colour. I would treat with louse powder anyway and see if it sorts them. Or, if you don't have one already, make your chickens a good dust bathing area and add some wood ash to it and see if they can sort it themselves.
Assuming she is over a year old, I would imagine the loss of feathers and drop in egg production with your hen is almost certainly down to moulting. I'm in the UK and my flock are almost all looking pretty shabby at the moment with moulting and egg collection/hunting (I free range) has become a very demoralising activity in the past few weeks!
Good luck with sorting your parasite problem. I've been fighting red mites for the past month in one of my coops and although I seem to be winning at last, the problem is taking a lot of bottoming.
Best wishes
Barbara
