When you go to the award ceremony you can click on the door and set the celebrity level lower.. or higher. My sim was a three star celebrity when I sent him. I didn't need to change the level but it was possible to do.
As for the other part .. I haven't played the active acting career yet but the interactions that give fame are pretty boldly labeled. Fame is a result of interacting with the public somehow on your sim or interacting through their work or things that become known. Even reclusive stars have to put themselves out there now and then. That's just the way it is.
You said yourself one of your stars is fame hungry.. so I guess that one is getting ahead because they are working the system?