To OP: you are getting a lot of advice here. Welcome to BYC and congrats on your new flock. Agreed, feather picking seems to be your primary problem.
You might want to do an info search re: mites and lice. Know what you are looking for, then do a thorough coop and bird inspection. Mites live in the coop and come out to feed on the birds at night, while lice live on the bird.
Increased protein will definitely be beneficial. It will help them to re-grow those feathers, and if they were plucking due to dietary deficiency, the extra protein will help fix that. What were they being fed? If they were on layer, do you have the bag handy so you can check the mill date? Feed older than 6 weeks has begun to go stale and the nutrients in it are rapidly degrading. If they were getting a lot of scratch (I'd not give it every day, and then only use it VERY sparingly) or other kitchen scraps that are NOT meat based, their diet may certainly be the cause of the feather picking.
Things to consider to improve their environment/health:
Fermented feed. There is a FAQ article in my signature (written by Tikki Jane) about the how and why of FF.
Deep litter in the run. An incredible plethora of health and nutritional benefit to be had by keeping deep litter in your run. Bare soil, especially in a chicken run is soil that is being mistreated! A deep litter draws beneficial micro-organisms, as well as beneficial worms and insects. It provides the birds with plenty of digging opportunities, feeds their guts with beneficial bacteria and fungi to improve their digestion and immunity. Birds on DL have better health, better feed conversion, less issue with behavioral problems. Bare soil in a run becomes dead soil b/c of the high nitrogen and Phosphorous load. Pathogens abound, and the soil eventually becomes so over loaded with N and P that it won't grow anything. A DL will be saturated with beneficial organisms that will convert all of that excess N and P to healthy compost for your birds and your gardens.
Ventilation in your coop year round. Recommendation is for 1 s.f. of ventilation per bird. The ventilation needs to be provided in such a way that the birds are not in a draft when perched. Your birds will not need heat... unless you are in a climate that stays below 0*F for days or weeks at a time.
Predator proofing: If there is a hole you could push a quarter through, a weasel can enter. A weasel can destroy a whole flock in a single night. Chicken wire will keep chickens in, but won't keep predators out. A buried skirt will help to keep digging predators out. While hardware cloth is much safer for coop and run, there needs to be a risk assessment: What is your tolerance for loss to predation in relation to your available funds to keep your flock safe??? Hardware cloth, bird netting, chicken wire, skirts, keeping birds shut up safely in the coop every night, perhaps a dog, having a gun handy to dispatch predators, trapping (Humane or to kill) hot wire around coop and or run. Some or all of these methods can be used to help keep your flock safe. Every flock owner has his/her own management style and loss tolerance.
