Taking into consideration everything you wrote, my bet would be on her being gifted. Don't worry about school for awhile. Just let her be a little one and have fun playing and learning as she plays. My DD4 was very challenging at 2.5: highly intense, opinionated, restless, etc. but also funny, enthusiastic, and charming. At that age she was beginning to read and to draw pictures that looked like what they were suppose to be.