"What does he wish from her?"

Translation: O que ele quer dela?

[Barbeito]

two points about the rejection of my attempt "O que é que ele deseja dela?"
1) I learnt from two other language courses to begin questions with "O que é que ...."
2) "quer" means "want" and "wish" I thought was "deseja". Here the suggested answer translates "wish" as "quer" Is this really correct?

[erudis]

You can use either "O que", "O que é que" and "O que que". They're all correct, but the last two are more colloquial and thus less used in written language.

You're also correct about your second point. The most accurate translation would be "deseja", but both "quer" and "deseja" have very similar meanings, just like "want" and "wish" (the former can sound more imperative though), so I don't see a problem in accepting both answers.