] Just wondering, what exactly is the Pump Room? The note in my NA says that they sometimes had bands there. Is it something like an assembly place? What goes on there?

Seems to me that people meet there and walk about. I'm not sure.
The Pump-room was most popular when the band played, that is, from one to half-past three.

] I remember people explaining this sometime last year, but I couldn't find the posts!! :o(

Well, I couldn't find them either, so sorry, wish I could.