I too don't have a daughter... let along a teenage one lol but this is how I would imagine I would deal with things.

Dye her hair: not until she can pay for it herself. My mum did this with me and it made me appreciate the cost of it. It also prevented me from colouring my hair till I was over 15 and had a job.
Shave her body: Most definitely yes
Get piercings: besides the ears, not until she can pay for it herself. And even then probably not as she will no doubt be at a private school which will not allow them.
Swear: Not in this house (though that means I will have to stop swearing myself lol)
Drink: I'm with rolymogs on this one.
Smoke: Never
Go out for the night: Up to 15 - sleepovers and friends supervised parties only, over 15 supervised parties, movies with either pick up and drop off by myself or someone we trust

Here's another one...

Would you let your teenagers go in the cars of her teenage friends?

Personally unless I know the friend and trust them, then no.