I have a question as I have been looking for the answer on Google, but I don't know how to phrase it correctly :P.
I am writing a little app for iOS using Facebook API. I would like apps to communicate between each other, not a lot, just a little bit of data, between users who use that app. Does Facebook support something like that or do I have to implement my own server side in order to have such behavior?
Facebook doesn't support anything like that. You will have to develop your own backend for something such as that. Each of the App's Users who log into Facebook, create a corresponding User in your backend database, storing the Facebook ID of that person. Now you're building your own database where you can handle relationships, and communicate with each other.