Here's the scenario:
Went out with some friends to a bar, and spotted a cute Korean girl sitting on the opposite end. I didn't put too much thought into as I was having a good time with the guys. I went outside to smoke and there she was with her friend sitting at a table, chatting and smoking too. I sat at the table around the corner and couldn't keep my matches lit to light my cancer stick so I went up to the two girls and asked if I could get a light. The cute Korean girl I was eyeing up gladly offers her lighter and compliments my shirt.

A few minutes go by and I decide to stand up and put myself clearly in her view. While she's talking to her friend I look around just to take in the scenery. As I'm doing this, she looks up at me and asks me if I wanted to sit down and talk to the two of them. I happily agree and we have a good conversation about random shit. As the bar starts to close down, the girls get up to go back inside to meet up with their friends so I tell the girl, "Hey before you leave, let me get your number" and close the deal. Score.

As the bar closes, my buddies and the two Korean girls and their friends all come outside. While this is happening, I go up to the Korean girls and convince them to go with us to grab a bite to eat. So we're all walking down the street, laughing, conversing, and the Korean girl randomly asks me if its ok for her to grab onto my arm. Here's where I fucked up. Instead of saying something cocky and funny, I simply said ok and we walked for a bit looking like a couple. Completely AFC, I know.

We got our food, and then parted ways. Here's another time where I fucked up. I was semi drunk and called her to see if her and her friends wanted to continue the night. She picked up and said she was going to drop off her friends, but I should text her later to see whats up. I told her no, she should text me.

Fast forward to the next day, I texted her with this:
"Hey Mickleton (where she said she was from), how are you feeling this morning or should you and I not talk about it? (She was saying Lets not talking about it all night and I was trying to tease her about it). No reply.

2 days pass and I decide to give it one last shot:
"Wow, already playing hard to get? One moment we're walking down South Street arm in arm and now this? We are moving way too fast and we haven't even gone out on a date yet!

She replies:
I'm sorry but I think you have the wrong number.

Haha, at this point I already know its time to move on, so I left her with this:
Oh thats cute. My 13 year old sister pretends to give out fake numbers too.

I'm not the type of guy to get hung up on a girl, as I was able to f-close a girl at a 4th of July bbq 2 days later within only hours of meeting. But I'm still interested to see what you guys have to say. Criticism is invited, I'm always looking to improve my game. How would you guys have reacted to this kind of situation?

You've correctly pointed out where you went wrong.

1) The arm thing. You should have asked her what you would get out of it, she'll usually ask what you want after laughing, or just laugh. If the former, get a kiss out of it atleast.

If I made this mistake right there, I would have walked slower, since she was on my arm, I could easily isolate that way, and it was an obvious IOI. Once isolated I would initiate the kiss sequence. Which for me is usually winning some sort of minor argument and betting a kiss.

2) When she told you to text her later that night, it wasn't time for you to be cocky funny with your "you should text me" line, it was time for you to tell her to pick you up after she dropped her friends off. She was obviously pretty sober if she was dropping them off/driving => you were in.

Now, if I had already made your two mistakes, then I would move on. Obviously she wants someone that is forward/confident, and she gave you many chances for it, but you came off as someone who was unable to f-close.

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Take notes.

Hey bro, sounds like you did good early on but at the end you kinda cared too much, it seemed afc.

"Hey Mickleton (where she said she was from), how are you feeling this morning or should you and I not talk about it? (She was saying Lets not talking about it all night and I was trying to tease her about it). No reply.
- def don't Text her the next morning, seems needy. Also I woulnd have pressed to much on what ever she didn't want to talk about , sounds like she was annoyed about that.

2 days pass and I decide to give it one last shot:
"Wow, already playing hard to get? One moment we're walking down South Street arm in arm and now this? We are moving way too fast and we haven't even gone out on a date yet!

- this doesn't make any sence lol I know what you were trying to do but u applied this the wrong way. It comes off looking desperate.

I don't mean to be mean just tryn to help, the best thing to do know is learn from the mistakes and know not to do the same next time