This is the same girl that sort of sits near you right? The fact that she spent a lot of time at the beginning trying to talk to you and then based on the way you responded would totally explain her behavior now. At the beginning you sort of avoided her, at least that's what I took from your earlier thread. It seems like you've been very inconsistent with how you've interacted with her, so she likely has no idea what you actually think of her and thus doesn't know how to respond or treat you now.

The fact that she still initiate contact with you, to specifically include you, is evidence that you're likely misinterpreting a lot. People don't invite others out if they have no desire to know them or find them annoying. Those are likely outings that you would have no idea even happened so she could easily have not invited you and not worried about it.

You asked if women can tell the difference between someone who is awkward socially and someone who has a crush on them? Sometimes you can tell but sometimes you can't. Usually you are going to base your actions assuming the worst. You clearly do that in social situations so why would it be any different for her to do the same? I Will definitely respond as if it could turn out badly, I've even been somewhat stalked by a few men. She may be worried about leading you on along with not being sure about what you want from her due to your inconsistency.

I agree with others in this thread that you can't rely on a group of people to give you an identity. You have to come to a group already having your own identity. It would be coming off as very fake to the most likely. They would likely interpret Your social awkwardness as actually just being fake. Which would probably make them question your intentions. This would make it even harder for them to trust you or want to actually include you and become proper friends.