I’m working on a project where we are developing an iPhone-/Android-app in which we would like to be able to integrate offline maps for a specific area. We would then like the user to be able to use the GPS within that area, to be guided from where he is - to a specific point (within the offline map). All this without having an internet connection. Would this in any way be possible with OpenStreetMaps?
Indeed this should be possible!
Have a look at the OSM wiki about http://wiki.openstreetmap.org/wiki/Android and http://wiki.openstreetmap.org/wiki/Apple_iOS
Try filtering the apps that are a) open source and b) use offline maps
Then tell us what app comes near your aims.
Also on http://help.openstreetmap.org there have been several questions similar to yours. Search for keywords like app android ios offline … or similar.