(1) 的 is implied, so you can omitted it. But either way is correct.
(2) 很 means "very". Now, you got a question asking "whose" tall is long, not "how" long is monkey's tail. So if you added 很 in your answer, you were not answering the question.
(3) I agree with Kaka, it sounds like it should be “长又长”, which means it's "very long". But to be honest, poem is different from everyday writings. They got limitation on number of words, and they have to sound right, and even matching certain words with the previous lines. So, I suggest you don't take it too seriously until you get a very good grip on the language and culture. It is difficult even for the natives.