The stuff around her mouth and on her chin sounds like kitty acne. I've never heard of kitty acne around the eyes, so suspect it is the Persian eye thing. To help get rid of the acne, use glass or porcelain feeding dishes, not plastic. And be sure to keep the dishes clean. I've used a toothbrush to brush the black stuff off my cat's chin and swabbed it with betadine. It can take awhile to clear up. Do a search for "kitty acne" on here and you should find lots of information.