Tips to make friends, win my crush over, and hint to her I'm a lesbian too.

Short Version: There's this lesbian I'm crushing on, but I'm still in the closet, have no friends, and can't seem to manage to make them and join her social circle, an introvert who actually enjoys being alone mostly, seen as the quiet, super smart, loner alien by my peers, turn to jelly whenever I'm near her, don't know how to flirt, and when I do try to talk to her I always think I'm bothering or boring her even though she doesn't give off that vibe.

Longer, detailed version:My first idea was to try to become friends in her circle, but whenever I try to join general conversations (not private, personal ones) I feel like her friends (not her) ignore me, and don't want to add me to the conversation. Every time this happens I feel like I'm a nusciance, boring, unwanted, and/or an alien. It's not just her circle either, it feels like everyone does me that way. Am I not speaking loud enough, adding enough to the conversation? I'm not shy, as I participate in class all the time, love to present, always willing to help someone out if they ask, on the debate team, and I keep a positive smile on my face 24/7 as I'm a natural smiler. I am a at a new school this year (Im a junior) and at the beginning of the year I (stupidly) turned down some invitations to stuff like study sessions and tailgates, because I prefer studying alone and dislike most sports and parties. People wouldn't judge me for turning things like that down right? I haven't done anything to hurt anyone in my classes, but be quiet, and answer a lot of questions, and make good grades that I don't brag about. Back to the girl, I would really prefer to talk to her one on one, but her friends are always around and it would be weird to ask her for her phone number or ask her out anywhere when we're just classmates. I have managed to talk to her once im class (she sits right behind me in Hiistory), but it was a minute conversation and we only talked about classwork (I don't know how to make conversation) She doesn't seem put off by me, but my anxiety gets to me and I always think "she's going to think I'm boring, I'm just annoying her, she wouldn't date me anyway." I always wonder if she would even date a black girl. :bang:

 

I've thought about helping her study and/or trying to have a private study time, but I'm not sure if she would feel comfortable with me alone being as though we're only classmates and only talked to her like twice. I'm not even sure how to adk or infer that without seeming creepy or condescending since I know she doesn't make the best grades. Sorry for being so difficult. >.<