Part of this question is, what if there is no proof of the going behind the back with bad rumors, and you ask the person and they said to go back to the beginning, and act like nothing is wrong before and after you ask if there is anything wrong and then say nothing is wrong, how to be friends if they are important? Should you check with someone who may have heard the rumor to find out? That would reassure if it happened. If it did, is there a friendship? Does checking about it ruin the friendship? If something did happen and you are aware, let the person know and they apologize and say to go back to the beginning, then act like your friend and tell you they are, does that ever work or is it over once and for all if that happens? Would she say and act like friends partly but leave things out so you realize on your own that she is not? Do you know if people would do that, for a long time? I think so.
I asked someone if she was my friend and she said yes, so is that it, how to test it out, can I ask if she is just acting that way? This is an important person you don't meet everyday.