You can use 5% sevin dust to get rid of the mites. Put some in an old pillow case, insert chicken up to its neck, and shake gently. This will coat the chicken in the sevin dust and contain alot of the mess. Or, you can use an old sock, fill with sevin and powder puff her all over...making sure to get all of her.
As for the illness, could she be eggbound? I don't have any experience with this but the symptoms sound familiar. Search for 'eggbound hen' in the search bar. There should be some great threads to help you out. I do know that the first step is to feel externally for a hard lump in the abdomen that could be an egg. Soak the hen in water water gently massaging the lump in the direction of her vent.
Has she ever been dewormed? This could also be a cause.
Good luck, hopefully more people will chime in with suggestions and help.