So, what is the thickness of the floor? Does the elevation of a level start at the upper surface of a floor, or does the floor 'fill up' the level from its base elevation?

Floors are added to the height setting of the level. In other words, if you set the height of the level at 8' and the floor thickness at 4" , the total height of the level is 8'4", with the 4" at sub-level.

Are walls drawn from the elevation of their level, or on top of the floor?

Walls are built on top of the floor.

What about ceilings? Do they have any thickness?

Ceilings are one sided so there is no thickness to them. Just a one sided poly.

E.g. I have an outside door in a wall. From where is its elevation calculated? From the bottom of that level, or from the floor above that?

Door and window heights are set from the top of the floor. The floor is actuall below level.

That also leads on to doors and windows. When specifying the width, is that the width of the actual door/window, or the opening in the wall?

Do you mean the depth/thickness of the doors and windows?
The default doors are 3' wide, 11 5/8" thick and 7' tall.