No you are wrong. The aircraft doesn't do anything automaticly.
in NAV it follows the route programmed into the computer by the pilot as long as all the route points are connected, if their is no route in this computer it will not follow it.
If the routepoints are not connected, a discontinuity, the aircraft will revert to a basic autopilot mode: Heading or Track depending on pilot input.
A star is nothing different then a bunch of routepoints, the aircraft doesn't know if its on a SID, STAR or in cruise.
So if there is no star, a pilot can build his own route, or use heading or track to follow ATC guidance or fly manually.
Many approaches are coded in the database, and they can be selected. For the computer however these are just another bunch of routepoints.
All the routepoints are contained in a database, which is validated. Anyway an ILS is not flown based on these routepoints but on radiasignals emitted from the ground.
An airbus does not climb or descent automatically without pilot selection.
Before you ask more questions I suggest you first get some more information on the basics of flying. Automatics are hard to understand if you dont know the basics.