There are five mini-riddles (one per couplet) each with a one word answer and then the five answers are further involved in a puzzle to find the final answer. Each couplet might contain any numerous kinds of plays on words like homophones, puns, double entendres, etc. (reading them very literally can be helpful). Ultimately though, I would call them what am I's. Here are a couple of links to similar ones from before:
PS - your second guess for the third couplet is on track...