How can I stop my sister from slandering my name for all to see on Facebook and posting photos without my permission?

Why would your sister want to slander you on Facebook to begin with? I think the first thing you need to do is talk to her about why she is doing this. Maybe the things that she is saying, she sees as teasing/joking and not really 'slandering/bullying.' Have you told her that what she's doing is really bothering you? Talk to her about this and be sure to have this communication in person (not on facebook).

If you talk to her and you are unable to resolve things, then you could report her behavior to Facebook. When she posts photos of you that you dislike, you are able to request that she remove the photos and you can remove the tag (that labels you in the picture) from the photo yourself.