"What does the animal eat" versus "what eats the animal"
It seems to me that "what does the animal eat" and "what eats the animal" would both be translated as "hva spiser dyren" despite having very different meanings. Is this true?
While "Hva spiser dyret?" technically has both meanings, you'd be more likely to rephrase it as "Hva er det som spiser dyret?" if you wanted to say "What (is it that) [eats/is eating] the animal?".
True. But in real life, I have never seen a misunderstanding. Context will give right result. Another phrase. "Hvem elsker Jackman?" might mean both "Who does Jackman love?" and "Who loves Jackman?". In any situation where this might give some room for confusion, I would use "Hvem er det som elsker Jackman?" or "Hvem er det som Jacckman elsker? instead.
So the animal is a subject in one and an object in the other. Without specific context it is presumed to be the subject (i.e. What is the animal eating). But as other answers say, there's usually context or you can be more specific in your question to clear up any confusion. "hva er det dyret spiser?" Is a more specific way of asking what the animal is eating (what is it the animal is eating?)
Hope this helps :)