I can't really tell you if you're being a bully
*,
HOWEVER, I don't think you have any reason to be mean or impolite. There's no way for you to know for sure what's going on in her life, and her actions may be her way of dealing with it. While I also don't know why she does what she does, I'm going to try to give a few examples of
possible reasons. It's possible she's looking for validation for her anxiety and other things because the people in her family ignore it. As for food, you have no way for sure to know whether or not she's eating enough at home. It's very possible that she could just be more hungry than embarrassed to ask for food. While it may appear obvious to you when someone is fake crying, this is something you can't know for sure. Sometimes it may appear to be fake while it's actually real. Even if she is crying on purpose, there's a reason behind it. I think more than likely she
is having a really hard time, whether she was crying for real or not. You're going to have to be around people that annoy you your whole life, and more than likely you're going to have to work with them.
I would say the best way to turn down her hugs would be to just
politely tell her that you're uncomfortable with hugs and would appreciate it if she respects your boundaries. As for not being her friend, you don't have to invite her to hangout and stuff but you also shouldn't be mean or rude.
*There's more to being a bully than someone being rude or mean. There has to be some sort of power play at hand and it sounds like you just find her actions annoying. If the entire school is outwardly being mean to her, repeatedly, or rejecting and humiliating her then this could be bullying. Which would make the participants bullies. I think
this link highlights what makes a bully pretty well