I know that you cannot delete the apple pre-installed apps on the iPhone unless it is jail broken. My question revolves around the actual phone app that sends/ receives calls. Does ios6 have any APIs that allow you to interact with the phone other than send numbers to dial? Is there a way to have an app intercept incoming call details?
No there is no way with which you can access call details. Since calls is itself an application and in iOS you cannot access other app's data from your app.