"What is the question?"
I'm not a native Turkish speaker, so this might be an oversimplification, but here's how I understand it:
It is customary in Turkish to use the "-dir" ending in the third person if you're describing a general fact or principle instead of a specific case. For example:
"Çay soğuk" = "The tea is cold" is a comment about this particular cup of tea.
"Kuşlar hayvandır" = "Birds are animals" is a factual statement about the classification of birds.
As for "soru ne?" and "soru nedir?", the latter might be used when asking about a specific fact: "Hamlet'in monologuda soru nedir?" = "What is the question in Hamlet's soliloquy?" There's a standard, factual answer.
"Akındaki soru ne?" = "What is the question on your mind?" I'm asking about your thoughts, but not suggesting that there should be a single correct answer to my question.
I hope other people will help clarify if I'm mistaken.