"Whose bear is this?"
Translation:Ποιανού είναι αυτή η αρκούδα;
Yes, in the general case, you'd use the generic masculine for the owner and thus Ποιανού;
These genitives don't agree with the possession in gender, number, or case.
So you'd use them even if the noun phrase is e.g. the object (for example, Ποιανού αρκούδα είδες; "Whose bear did you see?" (subject = you, object = whose bear).
Duolingo aims to teach words and syntax in each sentence so that you have the material to make your own sentences. Sometimes, the meaning is odd, as here, but that is encouraged by Duolingo to keep some humor in the course but also to keep you on your toes.
There are whole sites on the internet with "Funny things said on Duo", Facebook, reddit, twitter ...
"I am an apple." is popular on many courses, I've also seen "The bear is drinking beer." " I want to change the boy for a black cat." These are just a few I remember from the other courses I've taken. "The night club sells parsnips."
Ο οποίος in all its forms is used when linking sentences whereas Ποιος in all its forms is used for interrogative sentences.
Ποιος είναι αυτός ο άντρας; = Who is that man?
Αυτός είναι ο άντρας ο οποίος μου μίλησε χθες= This is the man who talked to me yesterday.
Ποιανού/Ποιου είναι αυτό το σπίτι; = Whose is that house?
Αυτο το σπίτι ανήκει στη γυναίκα της οποίας η κόρη είναι συμμαθήτριά μου= This house belongs to the woman whose daughter is my classmate.
Για ποιον είναι αυτό; = Whom is this for?
Αυτο είναι για το κορίτσι που αγαπώ = This is for the girl whom I love.