Is my friend schizophrenic or just a liar?

OK first of all she is not schizophrenic because that disorder involves a lot more and is a lot more serious. However "Jane" sounds like a person to stay away from. Maybe you should talk to HER parents about this and tell them everything she has said and show them any texts or facebook messages from her. It really sounds as though she has a severe case of depression so don't be too hard on her because no matter how crazy she acts, she wouldn't be this way if she was in her normal state of mind. Get her some help, get her parents to put her in counseling session but maybe it's a good idea to stay away from her because it's not your responsibility to pull someone out of a mentally dysfunctional state, leave that to the professionals.