The absent tail feathers makes me think she's molting. Hens molt seasonally and they quit laying while they do. With the shorter days, you may be waiting until February for an egg. Supplemental light would shorten the wait.
If the missing head feathers have to do with the molt or were plucked by another bird, she'll get them back. But if she is scarred, there's nothing that you can do to force feather growth.
I can't see the legs all that well but do they look rough to you? If the scales are sticking up, you'll want to treat her for scaly leg mites.
Age is super hard to judge on a grown chicken. She's an adult and a she, at least. If the feet/legs are as rough as the peek I see suggests, she may be older but it's also explained by a heavy infestation of scaly mites.