What is the most common length for stair nosing to overhang?
1" to 1-1/4" is fairly standard regardless of location, but it's mostly personal preference. You don't normally consider the nosing when working out rise and run, as they typically only apply to the stringers (which have no nosing).

Even if the nosing was considered, the rise and run don't change since you'd measure from one nose to the next.