Welcome to the forum mate, but the general etiquette is to post a message in the introductions thread before anywhere else.

If I'm honest, your trying to idealise far too much on how you think an 'alpha' would act, when you should be acting like somebody who's comfortable with the situation, or more importantly, yourself.

Not texting back, doesn't seem that much like 'bad behavior', you may be reading too much into it, she may just be texting her friends while she's out, trying to find out where people are, she may just be appearing online because her phone has signal. Or she may be getting guys numbers, point is there's not much you can do about it without being possessive just let it be.

Do you text her when your on a night out?