"The animals have questions."
Translation:לחיות יש שאלות.
With "יש" you wouldn't use the prefix "ה". When showing possession, you use the prefix "ל" with "יש". Thinking of it as "There is to..." helps. So, if you think of "The animals have questions." as "There is to the animals questions." it can help even though that's incorrect English. :) Does that help you?
I might have accepted it, but there is a good reason not to accept it. It's not a natural word order for the English sentence (it can pass in some very special contexts). Actually the word order you suggest is more natural for another meaning, "There are questions for the animals" (i.e. the animals are expected to answer).