Mouth, I wish I could provide something concrete. However I cannot find any other references to either of your questions in any of the books. My eyes are bleeding from me poring over the text, alas!
However looking at various maps, it seems your conclusion is an intelligent one.
As is your 'self' answer regarding the North Gate. Mentions of it are made earlier in Chapter 11 A Knife in the Dark, however it is of no help. Again maps tend to show the bridge to the east of the river.