How many minutes a day should an 11 year old girl tan in the sun?

Depends on your latitude. Probably between 8-12 minutes, after that, put that sunscreen on and wear a hat. You definitely want to protect the skin on your face. If you tan too much when you're young, you'll create premature wrinkles so when you're 22, you'll look like you're 35, and when you're 35 and not to mention the increased risk of skin cancer.