Can I start an online business at age 17?

The place you might have a problem is Paypal. You need to be 18 to have your OWN account there. But if she is willing to set up the Paypal account and allow you to use it (or give you a 'student account' there, which you should check out), you can probably make it happen. Just be sure that she knows the ultimate responsibility is HERS until you turn 18 (at least in the US). This is because only adults can make legally binding contracts - and that is what sales are, binding contracts.