] ....I'd always thought the Upper Room was the 2nd level of the Assembly Room and the Lower Room was the main floor. Why were they referred as such?

Bath is very 'hilly' and to get to the Upper Rooms I seem to remember you have to walk up quite a steep hill, so I assume that's where the name comes from. I'm not surprised you thought that the upper rooms were upstairs, though. It was a logical assumption!

] Also, this passage from NA chapter 2 added to my confusion, and confuses me still: Still they moved on--something better was yet in view; and by a continued exertion of strength and ingenuity they found themselves at last in the passage behind the highest bench.

There were indeed tiered benches provided (bleachers for the Americans!) so that the non-dancing 'audience' could observe the dancers below. In Rowlandson's 1798 print of the Rooms, you can see that those sitting against the far wall must be on such raised benches. I've seen prints showing much higher and more complicated tiered seating arrangements, but naturally I can't find any right now!

By the way - the print below would have been exactly contemporaneous with Catherine's visit to Bath. Jane Austen apparently used the calendar for the year 1798 to structure the novel.