You had not applied the rotation to your object. Since you had rotation amounts in each axis field, it caused the lid to rotate in the wrong direction when you tried dragging only one field in the properties tab. It was causing it to rotate on the object's local axis.
You can apply the rotation by selecting the object in Object Mode, hitting ctrl-A, and selecting "Apply Rotation." Now, if you use one of the fields to rotate the object, it will rotate as expected, on the global X axis.
As for the axis object that you wanted to get rid of, it turned out to be an empty in your scene, which looks like was the parent of the case objects. Just delete that if you want, or, if you want to keep it, just hide it.