There are several reasons why they would peck at each other. Certainly lice/mites can be a problem as you mentioned. You need to physically pick them up and visually inspect them closely, especially around the vent area. Mites are slow movers, look like pepper, are usually on the skin. Lice move quicker and easier to spot. Overcrowding can cause picking, is there enough room in their house for them to roost...enough room in their pen/run? Do they have the proper feed to eat? If they are over 18-20 weeks old they should be eating layer feed with at least 16-18% protein in it. Lack of proper nutrients and minerals can cause picking, treats should be only given at minimum including scratch. Picking could be a lack of enough protein, especially if they're eating the feathers. If that's the case, I recommend that you feed them scrambled egg with buttermilk mixed in their feed to make a mash and give it to them to eat for about a week. Another reason for picking could be boredom. Hang a head of cabbage in their pen somehow and let them peck at it. Hang it just a little above their head level. Your rooster could be overmating your EE, causing feather loss and bleeding, Perhaps purchasing chicken saddles/aprons will solve that problem. Vicks vapor rub or rooster booster "black salve" placed on the areas being picked will deter picking. Finally, picking and pecking could be caused by pecking order issues. If you can catch the aggressor in the act, you can seperate the culprit for about a week in lockdown, then return her with the others. She'll find out she's been knocked down a few notches in the pecking order and should end her aggressiveness.
