3) Sorry I don't know anything about ducks or quail.
4) The coop is the main home for a flock. It holds the roosts, nest boxes, and sometimes the food and water. The run/cage/pen is a fenced in place that is connected to the coop so that the flock can come out and find bugs.
This is my coop.
The brown structure is the coop. The fenced in pen is the run. The roosts and nest boxes are inside the coop.