So there are exceptions where we don't use "den" even when it's a living thing?
No, when talking about an owl, you would use "den". The "det" in the beginning of the sentence means "it" or "that" as an unknown entity (you don't know, so you are asking). Once you know it's an owl, you would use "den". So: Er det en ugle? Ja, den er sød. Is it an owl? Yes, it is sweet.
I can't think of a good example in English. Maybe: Is it a boy? Yes, he is sweet. Here you go from "it" to "he". Does that make sense?
Sweet means two things in English one is the food "sweets" and the other one is a personality which is like kind or nice
Breaking News: Sightings of A Green Owl from a website called Duolingo Spotted XD
The app should consider accepting "Is THIS an owl? ". It has not been accepted for me.