Hi, I'm new here and I have two things to talk about, and I'll try to be short. (That's what I learned here anyways. )
So, let's toss the ball around.

1)
So after initial contact via text (just one text), I would like to easy it up until I make a call and set up a date.

Do you have any suggestions on what to say?
Although this has been discussed probably gazillion times, I would like to avoid "let's rob a bank" or obvious lines.
And does the same rules apply like for IM as the SMS; like small number of texts, and to have some waiting time, like not responding exact second?

2)
Apart from this, I was wondering how to respond to rejected meet-ups? I left one conversation at that. She might have legit reasons and I asked for meeting the same day which doesn't help. Should I wait for her to contact me or not? I.E., do I look needy if I write her after being shut down?

One tip is to not ask them on the date in the traditional way. Ask them what they are doing on Saturday after 8pm. Something like that. It kind of puts them on the spot and often times they'll say "Not much" and then you'll know that time slot is clear and you can ask them out. If she is busy and says "Why do you ask?" You can even go as far as to tell her there is a cool show on TV you wanted her to watch. Then it won't seem like she was preemptively shooting down your date request.

As far as setting the stage for a meetup, beat around the bush and get her to ask about it first. Tell her "We should meetup sometime" but then don't elaborate on that idea. Let her come up with something. Or tell her that you are planning on going to a ballgame or a concert or to see some movie, but don't mention inviting her. Let her say "Oh, I've always wanted to do that" and basically invite herself. Then you could follow with "Well you can come along if you want, I can try to find an extra ticket."

You can easily paint yourself into a corner by saying "What about friday, no. Okay, what about saturday? No? Crap, ok, what about next saturday? .....NO? Oh jeez, will you ever go out with me???" Avoid that slippery slope of neediness.

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“Nothing is impossible, the word itself says 'I'm possible'!” ~Audrey Hepburn