I went to a salsa club (my first-ever salsa experience) - I did some things right, and a lot of things wrong. I've come up with ideas of what I could do better for next time if I'm in the same situation, and I'm sure your insights would help me big time! Background: mid-20s, good humor, bad with women, and a mega over-analyzer as you'll soon find out

Don't stress about my over-analysis, I went overboard remembering as much as I could and am hoping it helps you to give me your thoughtful opinions on the matter.
I went on Thursday night to a local pub that offers free salsa lessons for an hour, followed by latin dancing all night. I forced some friends (two couples) to come with me, so the 5 of us took the free lessons in a group of about 20. I wasn't dressed up as well as I could have been, but looked decent enough that night (my height and build helps).
I was doing alright during the lessons, getting the hang of most of it pretty quickly, but getting a little confused for the difficult moves. I had a feeling we'd be asked to pair up later in the lesson, so I took a mental note of where the girls around me were. I noticed that there was a group of 3 (2 girls, 1 guy) behind me, so there would be 1 girl looking for a partner. When the instructor asked us to choose partners, I quickly turned around to her and asked 'partners?' - she said 'sure'. (There was really no threat of rejection during salsa group lessons - all I really scored was a temporary lesson partner - but nonetheless, so far so good.) It was then that I realized she's gorgeous - not playboy hot, but sexy and adorable - the kind of girl we're all here for!
The instructor announced a 3-minute break in between when we were asked to choose partners and when we were to start dancing. We were told we could enter a draw in the meantime to win free salsa lessons.
- My mistake: Feeling awkward about not knowing what to do, I turned away from her to listen to the instructor's announcement, then went up and put my name in the draw, then chatted with my friends until breaktime was over. She was with the guy and girl she came with (who seemed to be a couple).
- What I should have done (or not?): Said "Hey since we're gonna be dance partners we better get to know a little about each other!", introduced myself to her friends, then taken her to enter the draw together, then chat until the lesson started.
- Why I didn't do that: I felt like she could interpret it as slimy for me to start chatting her up when all she did was accept my request to be her dance partner - I felt like she could be thinking "Seriously, I just need a dance partner, I don't wanna have to sit through his 'game' now?" But the main reason I didn't do what I should have done is that if I'm a cool guy who's out to have a great time, when there's a break why wouldn't I go and talk with my really cool friends - so that's exactly what I did. (i.e. What has this girl I've just met done to keep me sticking around, when I've got cool friends I could go talk to - I'd come across as a fake and she'd see it as a direct attempt to hit on her)
When we faced each other before the dance started and were listening to the instructor describe what would happen, she took the initiative of extending her hand and introducing herself - I then shook her hand and gave her my name, which she repeated back to me. After which I said "It's nice to meet you"
- My mistake: I didn't introduce myself to her first, she had to initiate the introduction. Also, I said "It's nice to meet you", which came across very awkwardly, almost too formal and as though I had nothing else to say (and even though it's a small detail, I feel like you shouldn't say it at the beginning of an interaction because you really don't know enough to say whether it's been nice to meet that person)
- What I should have done (or not?): I could have had something interesting to say - she introduced herself perhaps because I wasn't really saying anything. If not that, I should have been the one to initiate the introduction. When she extended her hand, I could have made a joke like "We're not business associates" and given her a hug (but since we were listening to the instructor speak simultaneously, I wouldn't have been able to do that - and hugging her that early in the interaction would seem a little goofy and try-hard - not to mention that making a joke of her initiative to introduce herself would come across as socially retarded and unaware). And finally, I shouldn't have said "It's nice to meet you"
- Why I didn't do that: I didn't want to start talking with my partner because whatever I was saying would be cut off by the dance instructor resuming the lesson. Next time I shouldn't care about being cut off and just start talking with the girl I'm with, because it's better than her having to fill in the silence, which is what she did.
Other things that were said:
- While we were dancing, she asked "So who dragged you here?" and I said how I was here with some friends and that I was the '5th wheel', to which she replied mouthing a silent 'Awww' - I took this as a small sign of interest. Looking back on this, I feel like I shouldn't have lied and should have said that "I wanted to try something new so believe it or not I was the one who dragged my friends out" and been proud of my initiative - I could have even joked about it and said "I bet you think I'm way less cool now than I was just a second ago!"
- She then said how dancing was a good skill to have, and I told her I agreed and that I can't dance apart from some cultural dancing I do, which she seemed impressed by (or she was just being polite)
- While we were dancing, I commented "This music is so festive!", trying to demonstrate my personality and ability to appreciate things like that
- It was her second salsa lesson, so I told her how she'd be the one teaching me
- While dancing, I commented on how we were doing really well and that they were going to make us the instructors
- I joked that since we were doing so well we should try some advanced moves and asked her if she knew how to do a backflip (didn't get the quality of laugh I expected)
- I told her how I was kind of impressed with how well I was doing (in a cheeky way)
- When our instructor came by (a decent-looking girl) to check up on our form, I bantered with her for a sentence or two while dancing with my partner
- When I started to lose rythym and was bumping into my partner's feet, I apologized and said my great skill from before must have been beginner's luck - she responded with 'Aww it's okay'
The lessons
The dancing eventually became monotonous because we were just rotating through the same 3 moves we'd been taught over and over. I didn't know how to lead the dance, because it was my first time, so I was discouraged by seeing other people on the dance floor mixing it up and having fun, while we were robotically doing the moves we'd been taught - I almost felt like a drill instructor "ok, side step"...then after a few moments "ok, basic step"...etc.
Please suggest what I should have done here. I felt like as the man I should be the one leading the dance, so that's why I was saying what step we should have done. But it felt robotic and unexciting. And I didn't feel like I could do much in that moment, because we were still bound by the dance class so I couldn't say "Hey let's go over there and talk" or "Let's grab a drink!".
After the lessons
As soon as the lessons ended and the dance floor was open for latin dancing all night, I found myself standing next to my partner and both her friends. The guy of the group said to both girls "Let's grab a seat" - she waited a second then said "Ok it was nice meeting you", to which I responded "Nice meeting you too", and walked back to my friends. I saw her on the dance floor twice again with two other guys who definitely knew how to dance, but I didn't see them talking or getting close. I didn't know what to do here, but I feel like when she walked off with her friends initially I should have said "Okay, but find me on the dance floor later tonight!" - but even that doesn't seem like making the most of the situation. I had a vibe all along that she could have been interested...
My option once the lessons were over would have been to immediately start talking to her about non-salsa stuff (i.e. use routines or just have a regular conversation with her), but my hang-up about this is that she just sees me as a dance partner and now that the lessons are over, so is our interaction. I don't want to come across as that loser kid who says "Awesome so when are we going?" in a group talking about an activity to which he wasn't invited
I almost feel like she's thinking "You've served your purpose, now let me get on with my friends and my night" - I'd feel so awkward to jump into social conversation the second the dance lesson is over, when her and her friends recognize the lesson is over, and when I haven't built enough attraction/rapport up to that point to continue the interaction...AAARGHHH! Am I right about this?
Rest of the night
She was sitting on the opposite end of the venue most of the night talking with her friends, and me and my friends both noticed her looking my direction a couple of times. I didn't want to ask her to dance because I didn't know how to lead the dance properly, so it would have been more of the robotic garbage we were doing earlier. And I didn't want to go up and just start talking out of nowhere for no reason because that would be too random and obvious that I was trying to chat her up - after all, if I were having a good time with my friends how would I even notice that she hadn't left the venue yet? For me to notice her all the way at the other end of the venue would've come across as though I was seeking her out, wouldn't it? How could I have salvaged it at that point?
I felt like if she had been around when I left, I could have walked by her table and said "I'm planning on bringing some friends here next week, you should come - do you have Facebook?" I wouldn't even have been comfortable asking for her number, because I didn't do enough attraction-building to merit a number, but I felt I may have been able to ask for her Facebook without creeping her out.
Anyways, that's my story - I'd really like your thoughts, opinions, suggestions on how I handled things and what you would have done in my case.