Is "Что у него на уме?" possible?
Yes it fits here
I don't know, but "Что у него на уме?" sounds to me like "What's on his mind?" i.e. "What's worrying him?", whereas "What does he have in mind?" is closer to "What is he intending [to do]?"
According to the Tips and notes "Что он имеет в виду?" would rather mean "What does he mean?" which can be interpreted VERY differently from "What does he have in mind?"
Что он имеет в виду? разве не What does he mean?
Что у него в виду?
Is this idiomatic or is there a way to work it out?
It seems very literal to me, have + in + mind => имеет в виду.
why do i need to use на instead of в
Уме and виду are two different words? I used уме and was marked wrong, (уме is the main hint)