I want to monitor when someone moves to another place on the map in a MapActivity but I have no idea how to do that. Maybe some sort of OnMapChange() listener?
You can extend the MapView class to add the necessary map change event. http://bricolsoftconsulting.com/extending-mapview-to-add-a-change-event/
The post above shows you how to detect zooming and panning via virtually every way you can interact with the map: swipe (for pan), zoom control +/- (for zooming) and pinch (for combined pan and zoom).