Backstory: I'll keep this brief, but I can elaborate and fill in the details if you guys want. I'm [21M] a rising senior in college, and about 3 months ago at the beginning of summer break I went on a beach week trip. A group of 3 girls joined us and during this trip, I managed to talk to one of these girl [19F] alone face-to-face. It was a casual conversation, no flirting or anything like that. When it was time to go back home, I made up an excuse so that she'll give me a ride (I had another ride planned, but I wanted to spend more time with this girl since it was a 4 hour drive). Once her friends got dropped off at the city I was also supposed to get off, I made up another excuse to be with her for another hour in the car. She lives in a different city and I asked to get dropped off at our university, which was on the way.

One thing we talked about was classes and it turns out that she's taking a class next semester that I already took. Over the 3 months, she messaged me on facebook twice. The first time, she asked what textbook the class used so that she can get a head start on studying. The second time, after about 2 months, she asked if the discussion session of the class was required to attend (it often isn't so it seemed like a valid question). Each of these times, I answered her question but made no effort to continue the conversation.

I always meaning to ask her out, but since we live in different cities it wasn't practical until school started again. A few days ago I decided to ask her out but a lot of my guy friends said that it probably won't work out since she's out of my league but I can try anyways if I want. I didn't have her number so I facebook messaged her yesterday. I was almost 100% sure I would get rejected and I was nervous as hell. However, it turned out well. Here's our convo

Facebook message 1 - the fact she included a heart seemed a bit weird to me but it was definitely a good sign

Facebook message 2

Facebook message 3

Text message

This is my first time ever asking a girl out, so what do you guys think? Even though it worked out, did I get lucky or did I handle this well? What could I improve on or what would you guys have done differently?