Question: What's up with the chicken being crushed? I don't see how it could be fake. I assume it was an accident, but why would they continue like nothing happened? And why would they put it in the movie? And why haven't I seen anyone mention it?
Answer: It does appear to be unintentional (or at least, unscripted), but they continue because when you're shooting a movie, you don't stop until you hear "cut", and especially at that time animal welfare wasn't necessarily a priority. I'm guessing no-one was concerned about the chicken, and so didn't feel the need to do anything about it. It's possible the film was made without an animal welfare monitor on set. As to why it's in the movie, the whole "marching to the prison" sequence was probably handled by the assistant director (as shots like this, not involving the principals or any substantive dialogue, often are) and they may have only done the one take. Who knows, they may have thought the injured chicken added realism to the scene.
Question: Why was Cardinal Richelieu's costume changed from red to purple?
Answer: Red is the "color" of the holy church; purple is the "color" of royalty. Richelieu aspired to royalty, not piety.
Question: Is this the only Bond film where the title song is being sung by a character during the film?
Answer: As far as I can tell, yes. Unless you count "Die Another Day," where the singer of the title song (Madonna) appears in a scene, as well as the song being remixed for the party scene in the ice castle.
Answer: Robin Hood, while disguised as a stork, wouldn't stop shaking Prince John's hand and it was starting to annoy him. Prince John was also robbed by Robin Hood earlier in the movie so he wanted to make sure that the jewels in his rings weren't stolen again.