She sent someone over to ask "What's the date." Durr. Don't you get the hint?
She is certainly curious but she won't wait forever so get started. She wouldn't know if she really likes you because you haven't really given her much of a chance to get to know you. It certainly would help if you would just be you.
Try to remember she will probably just be the first in a series of girls/women you meet in your life. It isn't like you are asking her to get married.
Stop freaking out and try to be a normal as you can. It is like this for everyone at first. You have to take a risk and start somewhere or you will end up seriously weird because you are way overthinking it.
Forget about dreaming up how to make compliments because they would come out weird. Genuine spontaneous compliments will come out automatically at the right moments if you just relax. And one genuine compliment is worth way more than a hundred trite lines.
You probably will say the wrong thing at some point, especially if you panic about saying the wrong thing. The bigger deal you make of this in your head the more likely you will say something dumb. It happens like that. Just laugh and say how "that didn't come out right".
Ask her simple things about herself. And above all, listen to what she is saying instead of worrying what you are going to say. That is how you start to get to know someone. And remember, she will be probably just as nervous as you.
Look at what she is doing. She is sitting where you will be. So you could try doing the same sometimes. Don't rush. Hang out together a bit. If all is going well after a while and you are getting to know what she likes to do you could ask her if you could do something you both like together.
Remember to keep breathing and don't act desperate. Smile and enjoy her company.
Best of luck.