Question: What horse actually won the race that Lonigan bets on Lucky Dan to win?
Chosen answer: I watched this the other night and specifically listened for what horse won the race that Lucky Dan was running in. It is never revealed who the winner is, because while the fake announcer in the back room is calling the race, the F.B.I. agents raid the building. During the ensuing chaos, shouting, and gunfire, it is impossible to hear the broadcast over the noise.
Question: Why doesn't Howie try to escape when being carried up to the wicker man?
Answer: What's the use? He's surrounded, he can't fight everyone and there's nowhere for him to run.
He is also a fundamentally religious man and he believes that he is going to die and go to heaven.
Question: I'm not sure if he already suspected them at the time, but why exactly did Harry want to take Davis and Sweet to arrest the gangster?
Answer: Because Davis and Sweet demonstrated keen interest, skill and knowledge of firearms (particularly of Harry's .44 Magnum) when they first met. They were flattering Harry, probably in anticipation of inviting him to join their death squad. Harry was impressed and asked for them specifically, even though they were rookies, but he didn't suspect them of being the vigilante killers at that point.
Yes, he did suspect them. In fact, he suspected Davis from the moment he found out that Davis was the one who reported Charlie McCoy's death. He confirmed his suspicion about Davis after he compared similarities between bullet that killed one of the victims and the one he purposely misfired from Davis' revolver during shooting competition and retrieved it afterwards. He explained it all to Early Smith right after raid on Palancio (and thus unwittingly sealed his partner's fate).
Question: The police find the accomplice's body in the trailer. In the last scenes the same body appears in the trunk of the car before it explodes. How did it get there if police had discovered it earlier?
Chosen answer: The police never find Harman (the dead guy). Charley was hiding outside the trailer when Harman was killed and he's the one who found him and took his body. When the police bust into the trailer, no one (dead or alive) is there.
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.