Did I just blow my chances with her?

I think I messed up the possibility of dating someone by making the first move. I have been interested in a girl from my class for two years, and I kept thinking that she was attracted to me, too. I didn’t say anything for a long time, but a week or so ago, I just went up to her and asked her out to dinner. She reacted with surprise and politely declined, and I have been wondering if I did something terrible. I think I should have asked someone to introduce us first, instead of just jumping to conclusions about her interest in me. I don’t know how to undo what has happened and am wondering if I have lost all chances of getting her to go out with me. How can I make this okay?
You can do exactly what you think you should have done and ask someone to introduce you first. It is important to let someone get to know you a little before asking them out to dinner, and that is another thing to address. If she does have a conversation with you, apologise for springing the idea of dinner upon her and consider a cup of coffee instead. Making the first move is perfectly normal, provided you do it in a way that allows the other person to be as comfortable as possible. Take this slowly, give her time and space, and take a step back. If she refuses, you will have your answer. Choosing to go out with you is her prerogative and you have to accept that.

Would it seem odd if I added someone on Facebook and asked how she is doing without knowing her personally?
Why would you do that and assume the person will be okay chatting with a stranger? Some people are, but you should base your actions upon what your intention is. Do you want to get to know this person? If you do, an introduction is more polite, along with context, instead of a question.