If she's losing feathers when she shakes, then likely molting.
I don't see anything concerning about the vent. Wet feathers always makes skin show.
If she is molting, then likely this is the reason for her going out of lay. She's lovely. As long as she's eating/drinking and active, then I...
If you feel she needs a cleanup, then do it. You may get by with just trimming some of the poopy feathers until the weather warms. If you give her a bit of a wash, then trim some of her fluff and give a good blow dry before putting her back out.
Since she's had issues all her life, she may...