Some more possibly helpful facts/advice:
1- You must take on being this person's employer, which means you are responsible for paying his/her tax and yours. Many people advise that you should pay him/her in gross. But there is no law requiring you to do this (I don't). A great website for sorting out what your responsibilities are is nannytax.co.uk (although there is a competitor called nannypaye who is cheaper)
2- Interview questions and reference checks are SOOOOOOOO important. Definitely follow up. A good book, which you can find at Waterstone is The Good Nanny Guide. Definitely read the chapter on interviewing/hiring.
3- "Au Pair", "Nanny", whatever you feel like calling him/her is up to you. If he/she comes from the EU, they can work as many hours as you want them to (within EU employment law of course).
4- If they live in your house, you are obligated by law to pay them minimum wage. If they don't, then you are.
4- Anything that is related to childcare, household duties, cleaning, running errands, laundry, etc. is fair game for reasonable duties (within the pre-defined hours of course) is fair game for an au pair.
5- She may also ask you to send her to language class. This is not required, but is common so you may want to pick up the tab for this if she asks.
6- Personally, I think that if you are taking a young girl from a foreign land into your home to live as part of your family you should personally pick her up at the airport (not just pay for it).
7- If you hire a teenager, expect her to act like one! If you are not looking to bring another child into your family, consider looking for someone older.