I'm a little unsure about how you actually find what zones are at range 1, 2 etc.
If it's just a matter of moving outwards from the zone of noise then I don't get why the yellow zone is 3 away and not 2. Do you not count diagonal?
The rules say that Zone radius is found by counting all zones that share at least one connecting edge.
I'm assuming this is meant to mean zones that share at least one connecting edge to the room that generated the noise?!
Yes - rooms/zones adjacent to the Noise are range 1, room/zones adjacent to them are range 2, and so on.
No diagonal moves in this game - for miniatures or Noise.
Some zones have very narrow overlaps. Adam rules that if the connecting edge is smaller than the base of the smallest miniatures, don't consider them to be adjacent at all.
If so then I don't really get the pictured example on p.7. as the zones above and below the Marine doesn't actually have a connecting edge to the room with the Marine. The room zones above and below the Marine only has connection with the Noise Zone through a second room that links them.
Noise travels through walls. The room to the 'north' of the Marine shares a wall with his room, so it has a 'connecting edge': it's adjacent. Same with the room to the 'south'.