What is the job of the post-production supervisor?
They oversea various editing tasks, assign roles, and decide what scenes get edited by who.

As a director, what tools will you use to assist you in communicating your individual style with the different artists working on your project?
You can give them sizzle reels, cuts of other movies that show how you want yours shot and cut, photographs, music, etc.

Describe in detail the duties of an editor.
They take all the raw footage and organize each scene then cut the shots of each scene into a final cut of the scene.  Then they use transitions between each scene.   There is also color correction adding LUTs to give it a look and feel, changing saturation and fixing lighting issues that may occur between scenes.

What happens when you have a final cut?
The sound designer comes in and makes the sounds and the composer comes in and makes the music.

Why is it important not to micro-manage your post-production team?
It's better to back off and let them have the freedom to be creative.

What was originally meant by the word "montage"? What is meant by it today?
Editing.  Today it is when a series of shots are edited together into a single sequence, often with music, to condense space, time, and information.
Who developed the "theory of montage".
Filmmaker Sergei Eisenstein developed it to mean a discontinuity in graphic qualities, such as violating the 180 degree rule, and the creation of impossible spatial matches.  i.e. The ability to tell a story in a way quite different from how you would if you stood there as a participant.