Other than colloquially are there any more distinctions between using "to" and "być"? "To" is not a verb, so it's difficult for English speakers to understand just how it is used here. The case is not accusative so it is like the whole phrase "kaczka to ptak" is the subject in the sentence. Also if the word "zwierze" does not include birds it has a different meaning than "animal".
Yes, but this is the wrong case.