Is it possible that she is doing this for attention? Oh wait I just read were you mentioned that....duh!
It really does sound like it is more of an attention grabber, my little brother who is 14 is bi-polar, add/adhd and really a lot of what your suggesting is not quite the same symptons. I would suggest that when she is in one of her moods to ignore it completely, let her know that you will come back and talk to her when she is done, and ignore whatever becomes of your reaction to her, if you ask her a question and she slides around the answer do the samething, "I will come back to you when you are ready to give me the answer I know you know and thats the correct one" something like that.
I would also suggest finding some activities that would help boost her confidence, because she does sound like she is lacking in that area, maybe a basic dance class or something in an area she likes, and when she does do it right let her know how well she did, don't over praise cause that can lead to other problems but just let her know she did real well.
My oldest does have some learning disabilities, and acts a lot like your daughter, these are just some thing I did with him, and they do help, it takes a little patience in the beginning but by not giving into him helped move us past it.
I hope I helped a little.