There is no "direct" notification to achieve this but, while the Fbx scene is "alive" in memory, you can check the number of allocated objects (FbxScene::GetSrcObjectCount()) and if the number is different from when the scene has been "created", then you know that some objects have either been added or removed. Almost all the FbxClasses derive from the FbxObject so the above function will "catch" a lot of objects of the scene.
For properties changes, you may be able to use the FbxObject emitter functionality. It will emit the FbxObjectPropertyChanged event.
But for anything else (for example: vertices coordinates changes) I am afraid you will need to implement some sort of lookup tables that "collect" the initial values (right after the scene has been created/filled) and that you will use to compare with the current state of the scene at the time of saving. But it may quickly become an overkill process 🙂
