Here is an article that looks like it has a lot of good information in it. https://www.backyardchickens.com/articles/mites-chicken-pests-how-to-protect-your-chickens-from-mites.47721/
Yes! Hens can molt at any time but very often (more often then not) above a year of age.
If you suspect mites or lice take a look at their skin, for best results, look around the uropygial gland (preen gland) and around the vent. Look in a dark room and try using UV light.
Does it look like a...