I think the above is great advice.
If you want to keep a door to a friendship open, tell the truth about how you feel. Your friends will either accept your honesty, or they won't; in other words, if they don't appreciate where you are coming from, then you should consider what type of friends they are - understanding friends, or not. Stick with the friends who like and enjoy the same things in life that you do, rarely will you be let down. Regarding the people who told you they have never liked you, well, not only have they wasted your time but theirs also; count it a blessing that you no longer have to deal with them again. A true friend will never make you feel like you have to stick up for yourself in their presence.
Taking Karate is a great life lesson; not only do you learn respect, self control, and how to defend yourself, but you have learned how to walk away from a fight, deflect the punches & kicks - this can apply to everyday life, even if it is a simple disagreement. Don't let anyone take advantage of you, respect yourself (and your opponent).
Take Care!
It's ok to be shy. But if you want to change it, get a bit radical about it.
Really just step up to the plate and pretend like you don't care how people perceive you, and that you're completely comfortable being who you are (which is how we should all be). Sales people are often the most confident on the outside stereotype we first think of, but I can tell you, from experience, that they're often the most insecure. If they can seem confident, anyone can.
You may find that after high school, all of it will seem silly anyways. I suppose, if there's one message I could pass along, it's that none of the clique garbage will matter soon enough. Sure, there will be cliques in college, and the workplace, but you may find it to be very different than how it is in school. You will soon have a new identity, and you'll find that after high school, more people have "real" personalities, because they stopped worrying about who they were supposed to be, and became who they really are.
Of course, the popped-collared mouth-breathing types will still exist, but even they know they're just complete fakes. Well, maybe some don't, but they tend to be too low on the IQ graph to have a conversation with.
Be yourself, and be confident in who you are. People will respect it, and appreciate you not being a generic "wannabe". Just because some children acted rudely towards you, remember, they're just dumb kids.
Confidence in asking a girl out is as easy as this. When you get shot down, and EVERYONE gets shot down, don't worry about it, and say "that's cool, maybe some other time". Then completely ignore her, and move on. Now it's her move, or who cares.
/As far as shooting down your friend's offer, well, just tell him you wanted to go, but plans got in the way. Everyone understands that. No need to worry about it.