Ah, it sounds like that she has all of the power here, this is not a good place to be in. She seems to enjoy playing games, in which case it's important that you play games as well. I'll offer some advice on this.
You ask her out all the time and she says maybe? Simple, stop asking her out, you're coming across as slightly needy and too available. This is unattractive.
Don't concern yourself with the "heart broken" story, it's of no use to you and is probably an excuse. Discard it from your memory.
She asks you to call her and doesn't answer? Well, that's just bizzare. Don't call her, either ignore the request or send her a text saying you're a bit busy at the moment.
Shaky voice is bad, try to talk deep and smooth, practice makes perfect

probably should've gone straight for friday rather than "any day" as this suggests too available, not too much going on in your life i.e. low value.
Also to be honest I don't believe that she really does want to meet you for a drink, the "shall I let you know?" suggests that she's likely to flake. It might be a good idea for you to cancel it before she does, and put her in her place.
However this girl sounds pretty toxic, and generally rather unpleasant. I would avoid investing too much into her, as you're likely to be disappointed. She is obviously very manipulative and selfish. Do not be a doormat, it would be a good idea for you to be selfish as well. While I believe that if you follow my advice above you'll have a better chance with this girl, I think that you should definitely focus your attention elsewhere, and put this one at the lowest priority if you absolutely must continue to contact her.
Good luck
