Not to over-complicate matters, but I got the feeling that it would also be appropriate to say "Örülsz vagy sem?" Would this be a possible answer for this sentence? If so, is it different at all from "Örülsz vagy nem?"
It is correct too and no, it's not different.
i think the only difference is the context we use it in
Boldog is a Duolingo translation, why is it wrong?
Orulsz vagy vagy nem - why wrong?
Are you happy? -> two ways to go: Boldog vagy? (boldog = happy, vagy= you are)
or Örülsz? ( Örülsz is a verb, this alone means You are glad/happy )
Since Örülsz is a verb, you don't need one more verb.
"Örülsz vagy" is like "you are are happy"
So, you cannot say "Örül uj evet kivanok", only "Boldog")
I will remember this.