] I would like to know, just what a gallery is in a great house. In P&P, I thought it was structurally like a gallery in a theater: an elevated floor overlooking rooms below, (snipped)

I think there might be a problem with light in an arrangement like this. Remember that before electricity, no part of even the largest house was ever more than two rooms wide because windows were needed for light. This wouldn't be as much of an issue in a theater gallery because everyone's attention would be directed towards the stage and not on the walls around them.

] After reading NA, a gallery seems to be more like a hallway. Which is it? How did it look in the P&P movie?

I think the "hallway" scenario is probably more likely because it would do double duty as both a place to hang portraits and as a hall. Large windows on the outer wall would give plenty of lightk and doors along its inside wall would give access to rooms on the other side.