What threshold? I'm guessing other factors such as the fox's independent assessment of the rabbit's speed?

If the average rabbit becomes slower then the average fox will be more likely to estimate that a given rabbit chase is successful.

I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?

Not particularly. We haven't been quantising anyway and it reasonable to consider the overhead here negligible for our purposes. '

I don't understand this part.

You don't particularly need to. Just observe that rabbits running fast to avoid foxes is a stable equilibrium. Further understand that nothing in this scenario changes the fact that running fast is a stable equilibrium. The whole 'signalling makes the equilibrium unstable' idea is a total red herring, a recipe for confusion.