Hey Jonathan,
I am a teacher who is teaching unity to students.
You forgot to tell that translate gizmo when held from the middle doesn't tell you translate anywhere but it is constrained in two axises that intersect.
Red in Y and Z, Green in X and Z, Blue in X and Y.
I'll admit that it use to be that way but not anymore.
Also give a little info on 3D world: XYZ axises value is where your object exist, so every object has a transform component cause without it they won't exist also transform cannot be disabled due to same reason but other component can be disabled.
PS: I never knew about fly-through mode. So thanks. :)