The scaly legs are probably scaly leg mites. They are treated by coating them with something oily, or Vaseline, which smothers them. It helps to wash the legs first with a gentle brush. Treat everyone.
I'd also check for lice and mites around the vents or under the wings. Check at night, too, because some only get on the birds at night.
If you don't routinely worm them, they almost definitely have some, whether it's enough to make them sick or not. You aren't likely to see worms in poop even if there are a lot. One thing you can do is take a sample to a vet and see if they will do a float test for parasites. Not usually expensive, and many who won't see chickens will do this. I just give mine a dose of Valbazen once or twice a year, but I know there are worms in this soil from caring for other animals.
Some chickens get poopy butts just because they have such fluffy butts, the poop sticks. You may want to give her a bath now and then. Gives you a good chance to look her over well. Just put her in a basin or sink with warm, mildly soapy water. Usually they will relax after a couple of minutes. Rinse well and dry before putting back out in the cold. You can dry her with a blow dryer on low heat if you want.
I don't know that these will solve her problems, but it's a start.
http://ucanr.org/freepubs/docs/8162.pdf (good pics)