Super I know what you mean, mine is always always moving, I look away for a second and something will have happened.
She just cannot sit for a minuet ( well she can if engrossed in a film).
Mine has also recently started to madly assert what she wants to wear...just pick your battles.
I used to battle with her over clothing I find its much better to let them do what they want in circs as you describe then when they get cold they will regret it! Also NOT pushing has opposite effect sometimes, saying cheerily " Oh a summers dress today? What a good idea! Ok then...."
re demanding things I told mine that Father Christmas doesnt like greedy little girls, and she knows there are poor people in the world and I say that he likes children who appreciate they have the basics when some dont even have that, and if he hears a little girl with lots of things demanding....he wont like it and it might jepordise her xmas....
as for making a mess, can you get her to make less mess and tidy up after? or give her a space to do it.
money rewarding has been severly attacked on here but i do find - saying i will give her a pound for things or a magazine does help to positivly motivate her, then after a while she does it automatically anyway wihtout the money, although she does have a piggy bank.
so you could curtail demands in shops by saying....be good girl, tidy up and i will give you money which you can then buy things with...
anyway sorry for ramble been a long day.
deep breath!