[Nasrudith]

Replacement rate depends on the death rate to be precise. If humanity had stuck with three children per couple at most throughout its entire history it would almost certainly be extinct.

2 is only the replacement rate for 'literally immortal up until a certain date' - morbidly with a corresponding high death rate the number could be 'greater than biologically the theoretical biological limits'.

Binary town's birth rate would go down initially due to the loss of participation reducing the reproducing generation by half but the time between generations being cut by half would mean an effective doubling of the per person rate. Without knowing their rate of death we can't know what happens to their true population over time and it goes without saying that the assumptions will break if their reproductive strategies change yet again.