Well you're first problem seems to be a bit of shyness, coupled with a group that has already established a dynamic. What I'd suggest there is to see if there are any of the other students who share interests with you and introducing yourself through that shared interest. I would also consider taking on some activities outside of the school, where you'd meet new people as well. I was much the same as you at about that age, but when I made the effort to meet new people my shyness disappeared.
As regards the girl, oh to be 16 and in love (or at least lust). Well first of all being tongue tied is natural (and better than my situation, where I'd talk fine, but make absolutely no sense). You're young, and worried lest you say the wrong thing, experience will help there.
First of all try to find out if she is straight (also a mistake I made), and then that she's not spoken for. Then get to know her through common activities (which you're already doing). Then I'd think about asking her out for lunch, nothing fancy sandwich and drink, maybe a matinee (or other activity you both like), just as friends. From how that goes you should have a pretty good idea if she's interested. If so ask her to a dance, bring flowers for her, chocs for the mother, etc. and have a nice time. If she's not interested romantically, do not stop being her friend, you'll regret it.
Hopefully that wasn't all rubish and helps you. Just remember though we're all in the same position at some stage.