Zevahim 12: Designate Your Offerings (+ an example of rabbinic unanimity)

More on the timing of the slaughtering of the Korban Pesach - whether it needs to be done in the afternoon of the 14th of Nisan or whether the morning of the 14th works too. Also, a newborn animal and how it can't be offered and also can't be given as a tithe. Plus, the case of one who does wrong (eating forbidden fat), designates his sin-offering, becomes a heretic (so his designation is negated and the offering is disqualified), and then comes back to faith -- is the offering reinstated? What about someone who loses his cognitive abilities (at the same point where the first one became a heretic), and then he was healed - is the offering reinstated? Both cases are necessary, as the Gemara explains. What if the court rules that the fat isn't actually forbidden? And then retracts the ruling that it was permitted - is that offering disqualified or no? Plus, the time that all the sages agreed.