Interesting question and one I haven't really thought about. Ditto with my DD2.5. Everything on your list is my DD. Even as far as asking to play the violin. She loves the guitar (DH plays guitar and allows her to 'play'.) She actually is pretty good and has already started tuning the guitar. She clearly has the ear for music and a voice. And balance: she always had this freakish balance. Many a friend would comment on her balance from when she was a tiny thing. From the minute she could sit on her own she would lean back with her legs in the air and never fall backwards. Is she athletic? I really can't say. I still think she is a little chunky but she loves dance and it was recently pointed out to me by another mom how good she really is with it all. She also loves gymnastics.
The problem with the gifted argument is I can make an excuse for about everything on that list.
-Her fine motor skills are highly advanced for a 2 yr old, but of course they are. Her mother (me) is an artist.
-The music factor: It runs in her blood. Her grandfather use to play with Willie Nelson.
-Her balance and dance ability: Her father was a gymnast ranked in the top 10 in the state when he was in high school.
The list goes on and on but again I have no idea if it has anything to do with gifted so I will be watching the thread to see what others say.