Depends on where you live. Here in eastern WA, we don't get enough moisture to affect wood so much that it needs to be seasoned undercover or inside a barn/outbuilding of some kind. And I found that many people don't even appreciate that like Maple, can be easily split after 1 1/2 seasons. On the western side of WA, it's another matter...you ALWAYS at least cover your wood, or pallet it inside a barn/outbuilding etc. And most people that live there at least know that.
In answer to your first question, we always based a 'cord' on stacked, split wood. Now it seems like they're trying to figure cords just dumped into some wood trailer. I guess you could come close that way, but we always had it ricked up beforehand or at least stacked in the trailer so we knew what we had. The customer could see it stacked that way first, even if we tossed it into their yard.
Kevin