Princesses?

I think she'd be like most other teens. I doubt this would change her all that much. She might be spoiled, perhaps rebellious if she doesn't want the throne, but I think it all depends on who you want her to be. You know the character, you know what her personality is like. Put her into a situation and ask yourself how she would act/think/feel etc.

If there is a living king or queen, she might not have very many "duties" as you say. And whatever things she would have to do would change from year to year, culture to culture. It's all relative, really. I think The Princess Diaries series is a really good one for seeing how a modern day princess might act. There are lots of YA books on teen royalty. Go to the library and get some. They will probably be much more help than I am.

The present day British princesses Beatrice and Eugenie went to private boarding school (as did Princes William and Harry) and had no royal duties

Waylander is totally correct, I was a Royal Protection Officer for the Duke and Duchess of York up to and just after the birth of Beatrice. Young Royals have no official duties.