I agree with
@aart that your new pullet/hen doesnt look in Too bad of condition. Yes shes missing some feathers, but thats not highly unusual by the late summer months. Her largish red comb says she is an active layer. When pullets reach point-of-lay (usually around 5-6 months old), their small, pinkish-yellow combs enlarge and redden, but are still fairly small in size. By around 1 year of age, a hen's comb is much larger and brighter red. If your hen is older than 1 year, she will likely molt within a few months. Meaning she will lose and regrow all her feathers during the process, & you will get few eggs from her during this time. She looks like a rhode island red or similiar variety, but i cant tell for sure if her legs are yellow or bluish in color. (In one of her photos, legs look bluish.)
Also, it looks like she has a ziptie band on her leg. Hopefully it's not so tight that it has cut into her skin. Carefully cut the band off asap; you dont need it to identify her.
I would check her poop to make sure she doesnt have worms. Round worms are the most common; they are large, long, & easy to see with the naked eye. Might not hurt to deworm with a dewormer such as Safegard either way, since "farm" chickens are often exposed to/carry worms.
Hopefully your new pullets/hens will start giving you eggs very soon. According to her appearance as far as breed, she should indeed produce large/xlarge brown eggs nearly every day. (That is true the first year; after that, egg production gradually decreases).
There is a vast wealth of info here on byc, & fellow members will be happy to answer any questions you have. Good luck and have fun on your new chicken adventures!