OP - I used to work for a man like this and it drove me insane, I just needed answers to get work done!
However, I quickly learned that he need to know why I was asking the question, or he'd give me a nothing answer until he had the full information, including stuff I couldn't see he needed to know.
He'd also use answering my question as a way to 'chat out' all the options, not just do that in his head, then give me the final answer.
So in you melon issue, I'd not ask "who ate the melon" but give the reason for my question "Did DS eat the melon? He was saving it, was it you or DD, as then I need to sort some more melon for DS."
Your DH's answer doesn't make much sense, becuase the answer is really "no one ate the melon". You assumed someone had. You didn't ask "what happened to the melon? Because I need to know if DS ate it."
It's annoying and draining to always have to provide context and explaination about why you are asking the question thought - although as DappledThings said, often it's about people trying to give you the justification for their answer, not the actual answer - which is infuriating!