I would like to add a custom compass to the map or replace the current icon and items. Is it possible?
map does not give this functionality that easily replace compass with your custom image.
But one way is disable default compass via setCompassEnabled and draw your own. Use sensors to make it point in the right direction.
you can use following example to point right direction. see below link.
http://android-er.blogspot.in/2010/08/simple-compass-sensormanager-and.html