"animon" or "animojn" -- each has exactly one, right?
I think you're right; where we'd say in English "do animals have noses" to ask whether each animal has one nose each, in Esperanto it's "Ĉu bestoj havas nazon?"
Animals have souls. An animal has a soul.
However Esperanto is different in English in this regard. "Ĉu homoj havas kapon" is the way one would write "Do people have heads" in Esperanto.
That sounds more like a theological question than a grammatical one
Tiu demando estas debatata ekde jarcentoj. « Ambaŭ povas esti dirita aŭ diritaj » (Vaugelas)
It's seems a consensus has been reached in the comments here that this should be "Ĉu bestoj havas animon?", and yet the translation suggested is still "Ĉu bestoj havas animojn?"....what gives?
Seems either is permissable
As many as we do, so no
I got this wrong because I didn't choose both.