Answer

Do you mean the firstborn of a kosher animal? It is not offered on the eighth day, but rather within the first year of its birth, as it says (Deuteronomy 15:20): “You shall eat it before the Lord your God year by year” (see Mishnah Bekhorot 4:1).
Perhaps you meant that the year begins from the eighth day after the firstborn’s birth, since only from that day is it fit to be offered (see Leviticus 22:27).

1. Once you wait long enough, there is no animal suffering here, since when animals grow up they do not remain with their parents. True, it has to be given to the priest earlier (after 30 or 50 days for small or large livestock), and perhaps that amount of time is also enough (I don’t know the nature of these animals). And this waiting period is not intended to avoid animal suffering, but so as not to burden the priest (see Mishnah Bekhorot 4:1). Perhaps the rationale of animal suffering is relevant here too, but since in any case they wait because of that other reason, the question of animal suffering does not arise in practice.
2. The question of veganism comes up in many contexts, not only this one. In fact, here there is no problem, since the offering is eaten by the priest and not by the owner. Only if the priest is vegan would a problem arise. But what will you do with all the other offerings that are eaten by their owners? What will you do with tefillin boxes, which are made from animal hide? And Torah scrolls, tefillin, and mezuzah parchments, which are written on parchment made from hide? I have no solution for all this (and I am also not bothered by the use of animals so long as there is no abuse and suffering involved), and we will have to wait for the Sanhedrin to decide.

Rabbi Kook writes that in the future they will not offer animal sacrifices, only plant-based ones, and that will solve the whole problem. We’ll wait and see.