Display List?

1. The way I understand it the stage is at the top of the hierarchy, nothing is above the stage any Display objects or Display object containers are children of the stage.

Really, the MainTimeline object is a child of the stage, and anything you put on 'stage' you really put in the mainTimeline object. If you trace(stage.getChildAt(0)) you will see object MainTimeline traced.

2. A movie clip on the stage (because of its nature to contain in itself graphics and other movie clips) are Display object containers, and any other movie clips in the movie clip are also Display object containers until we open enough movie clips inside other movie clips and find that the last one contains only a graphic, this last one is a Display Object, not a Display Object Container.

A MovieClip, or Sprite, is always a DisplayObjectContainer. A Bitmap, or Shape is always a DisplayObject.

3. If you have a graphic on the stage it is a Display Object because it does not contain anything in itself.

If it's a shape or bitmap yes, not a sprite or movieClip.

4. If you have a movie clip on stage is it a child of the stage?, Also is any movie clip and any movie clips inside another movie clip a child of the previous movie clip?, I read somewhere that it is correct to call some grandparents and great grandparents, what does that mean, that a couple of movie clips inside an original movie clip means the original movie clip is a great grandparent?

A MC on stage is actually a child of the MainTimeline, which is a child of the Stage. Nobody says grandparent etc. Child/parent is as far as it needs to go. Anything inside a container is a child of that container.

Something like this: .....

import flash.display.Shape;

var rectangle:Shape = new Shape();

var circle:Shape = new Shape();

rectangle.graphics.beginFill(0xFF0000);

rectangle.graphics.drawRect(0, 0, 100,100);

circle.graphics.drawCircle(40,40,100);

addChild(rectangle);

addChild(circle);

trace(numChildren);

I can't say whether or not the page linked below will help clear things up since the things you are trying to differentiate are somewhat interchangeable as far as terminology goes.

http://help.adobe.com/en_US/as3/dev/WS5b3ccc516d4fbf351e63e3d118a9b90204-7e3e.html

DisplayObjects versus DisplayObjectContainers might be considered like fingers versus thumbs... all thumbs are fingers but not all fingers are thumbs...  all DisplayObjectContainers are DisplayObjects, but not all DisplayObjects are DisplayObjectContainers.