The vent of a hen is where eggs are passed out of the body, as well as her droppings. Not being able to see or know the consistency of this liquid, I couldn't tell you what it is. It could be she is passing some whitish droppings or has diarrhea, it could be she is passing an egg with no shell and what you are seeing is the albumen or white of the egg.
This time of year many chickens are molting. I can't tell from your description how large or small an area she has lost feather. Chickens go through "hard molts" sometimes and lose a lot of feathers. It could be this is something else. If the skin looks normal, she should be growing in new feathers soon.
Hopefully she is active and eating and drinking well. If she is normal other than the things you've mentioned, she is probably fine.
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