You're doing well my friend! I am no expert here but I'll give my 2 cents to get the ball rolling.
Well, the first 2 sarges were not necessarily rejections because you didn't ask for their number to begin with, so don't put down yourself like that. I think you are playing the direct game approach, where your opener is to complement her. From what I can understand, being direct in openers would show that you are already interested in her. This means that the girl is already evaluating you before you can DHV or anything. From what I read, many PUAs (or PUGs) prefer the indirect approach, as most women would not likely suspect that you are interested in her, so she does not evaluate you superficially right off the bat.
For the openers, try not to use the same one for all girls. It is not really about originality (like the girls would know if your using the same line anyway), but more about the general idea. It would be easy and lean on the safe side and use the same openers, but by starting a conversation differently allows you to get a general feel of what works and what doesn't. That could in turn help you in other areas of the conversation, realising what is appropriate and what isn't.
The 3rd sarge was quite well done, you made a few jokes and funny comments that made her giggle (which is definitely an IOI). However, the close wasn't very well done in my opinion. You asked for her number, so just wait for a response. You don't need to tell her to be honest, and honesty is the best policy bla bla bla, cuz it actually DLVs you, giving the message that her talking to you was merely a polite gesture. I understand you did that because she sounded hesitant. Perhaps you can do a little C&F, like "Wow, I thought we got along so well, why are you hesitating?". It also sounds genuine when she said that it was nice talking to you, so I guess you got most of the game right! Also, when asking for numbers, I usually don't ask (the irony), but rather give a statement followed by a question like "I wanna keep in touch with you because you are an interesting person, how can I do that?" Most of the time girls like your statement so much that they just get carried away and answer your question immediately. There was once I did this and the girl just blurted out "you can call me", so I asked "Ok, what is your number", and I started sensing hesitation. But it is too late! She made the offer, she cannot retract from the social contract (it rhymes!)! So if you are not having much success by asking for her number directly, try my cunning method!
You did pretty good overall by maintaining a relaxed tone and make girls giggle. A better close (with more confidence) would definitely help you! Oh, and about the silence when she text thing, just try and sneak in a comment like "you always this busy?" and she would definitely give you a response. If you can't come up with anymore things to say, comment about how she looks so serious/concentrated when she text, then ask (in a funny way) if she needed help punching the keys. It is a nice buffer, plus, if she does give you her phone you can put your number in and call it (if you feel daring) so that she can get your number and you can get hers. It is a slick move that I learnt from my friend
say that you can't miss this opportunity for an "exchange" (or anything funny that would alleviate the creep factor, if she finds you so).
Hope that helps mate!
CHAT