Hullin 29: The Impact of the Collective on 50/50

More on the question of when a siman is cut precisely halfway across - is that 50/50 considered the majority or not? (it's still a machloket). With the parallel to the requirement that at least half of the population of the Jews need to be pure to be able to participate in the Pesach sacrifice. That 50/50 seems to be acceptable, rather than leaving a full half of the people to make up the sacrifice on Pesach Sheni (14th of Iyar). But as much as this example is brought in parallel to the shechitah case, they're also quite different. Also, when is the action of slaughtering actually considered to be an act of shechitah? From the beginning of the process or only once it has been concluded? The practical implication being for incomplete draws of the knife and so on.