Is there a possibility to see the changes in the graph editor while rotating an object (a keyframe in a curve changes its height) i.e. not when the object is already keyframed, but when you're still able to change its rotation?
The graph editor displays keyframed values. If you haven't keyframed a value then the graph editor doesn't have any data to display.
Similarly, as you move an object in the 3DView you are not altering any keyframed data so there are no changes being made to the data displayed in the graph editor.
Note that it does work the other way. After keyframing a value you can make adjusts in the graph editor and see the changes in the 3DView as you make them.