I have a 5 year old son who sounds like he has some similar characteristics to your daughter. He also will "pretend" that he doesn't know how to do things. At his meeting with the teacher before starting K, he pretended like he could only count to 12 and that it was difficult. Then, when she asked him to count backward he did it extremely fast. (He could count to over 100 by ones, fives, and tens.) My 3 year old son does the same thing. He'll pretend not to know letters and numbers he knows. But - for him I think it is still more typical. He gets bored and just "won't play that game." My 5 year old also will not write at school. He got "below grade level" in writing even though he is writing in sentences at home.
A little history - He has been diagnosed with RAD (reactive attachment disorder), high IQ, and SPD. (sensory processing disorder). He was diagnosed at the age of 2 and 9 months and we have worked very hard with him since then. He came to live with us at 12 months and we adopted him a few years later. Anyway - I think he has attached to us, but is still very oppositional. He also NEVER stops moving. It is exhausting. School is challenging, I am going to look at the information on the Active Alert Child. I haven't looked at that before.
Sorry - I don't have any advice. I just replied because I so rarely meet anyone that is struggling with some of the same issues we are.