I got 2 questions:
1. Is it a date, or not?
2. How to act on the „date“?

Back-story for question 1:
We're going together to evening-school (I'm 28, she's 21) and like each other. A little while ago we were talking in a group and somehow we talked about me being single. She said, she's sorry to hear, that it didn't work out. 2-3 minutes later she tells us, that she is in a 6-month relationship but hasn't developed any feelings whatsoever. So far nothing of importance.
Last week we chatted on facebook, I don't have a chat-log, but it was like this:
She: Give me your number
Me: , Damn, very quick in getting my number.
She: That's how we women are.
Me: Give me your number, too.
She: ,
Me: Damn, I'm good, I got 2 numbers
She: Yes, but you have to earn the third one
Me: Alright, I'll invite you to a cocktail sometime and then you'll give it to me.
She: yes, all right.

Note: At this time, I wasn't really single (complicated and not important now) and not looking for a date, just 2 friends going out for a drink. For that reason I haven't used any (of the little I know) PU-tactics. Now (actually since Thursday) I am single and Friday I asked her out for that cocktail and she said yes.
Now I was thinking, is this a date? She's very hot (HB9) and very sweet, too! I'm very interested in her, but I don't want to interpret too much. What do you guys think?

2. Since I was in a kind of LTR, I haven't actually used PU-tactics, I just learned some by watching Mystery’s show on MTV „The Pickup Artist“ and some other videos.

The date is on Friday, what do you guys recommend for me to do, to get her? I don't just want to get her into bed, my interest would be a relationship. What basic skills should I learn 'til Friday?

Note: I am pretty alpha, at least in school, where we see each other, I have that status.

Uh no fucking shit it's a date? To be straight forward, this chick wants your cock in her mouth, and you should think of it in no other way, if you think she likes you, she likes you.

As to how you should act after getting out of that LTR? Well the opposite of you dating her forever for sure. Keep your act Alpha, and make sure in any case that you show her how you role, be the leader in any situation, instead of asking her out to dinner, tell her shes going to dinner with you.

Be fun and high energy, no I'm not saying be like a little kid but make sure you enjoy the fuck out of yourself and she understands that. Use a lot of sexual context, when she says something, turn it into something sexual, this makes a woman turned on and makes sure she knows what's going on in your head.

Be simple and have fun, keep your frame, never let her win a battle of accusation, if she does what you want give her a treat, if she's bad, punish her

be cocky and don't let your LTR come out whatsoever.

Good Luck

Fender43

Thanks man. My "radar" is not very good at picking up signals like this, because I am not used to getting any signals at all in the past. Your opinion gives me much more confidence.
Do you have any examples as for turning something she says into something sexual? I usually talk open about sex, but I also don't want to be the guy who just wants to get her into bed.
Sounds great. How can I "punish" her? Let's say on friday, when we are at the cocktail bar?