I think at 16 you're entitled to some privacy, everyone in the world says things that they don't want broadcasted to the whole world (so why they'd ever post anything on facebook, I don't know, but that's for a different thread), I'm sure your mother occasionally says rude things about your behaviour to her friends but you're demanding taped recordings of all her conversations.
In the end, there's got to be a certain level of trust, and unless you've done something recently to alert her, and she has a reason to not want you talking to people without her knowledge, then you need your freedom.
Personally, I'd add her, then make a new facebook account with a whole new random name, and just tell your friends. (obviously don't post any photos).
Or just quit facebook, use your cellphone to stay in touch, or skype, or MSN or one of the other thousand options.