What about an app that would just track them down using their phone numbers, what I mean is find their location!
And some kinda app that wouldn't need any permission and stuff
You should contact the cell phone service provider. They can know current position of their subscriber. But I think it is almost impossible because of the privacy law. Applications like truspy require you to install onto the target phone, so it will not applicable to you.
There is a way actually: you give the person you want to track down your iPhone(with Find Friends installed and activated) as a present for her birthday and then you track down your iPhone. There you go!