Question: What kind of instrument was the bum playing when we first meet him?
Answer: Violin.
Question: When the boy enters the train car the other kids are heard singing the polar express song. How could they have learned it?
Answer: They likely were taught it before the boy boarded the train. We should assume that the same magic making the train appear without being seen by others and to travel to the North Pole is also at work here, perhaps allowing the children to be able to learn the song quickly.
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Answer: Alternatively, it could just be a song they all made up.
Answer: After "Hero Boy" gets back into the train the kids are all laughing and spouting gibberish. This is often done in post-production when backround noise or talking is necessary. They aren't saying or shouting anything in paticular, just a bunch of kids jabbering on about nothing. I listened to that section three times and it's just gibberish.
CCARNIQuestion: How come the conductor and the hero girl walk on the roof of the train headed towards the front when they could have walked through it, the way they did coming back with the hero boy?
Answer: Cinematically, it made for more excitement. Walking to and from the engine through the train is, let's face it, boring.
CCARNIQuestion: So if you can't hear the bell you don't believe in Santa, therefore if the parents can't hear (ie. don't believe) and Santa brought the presents who do they think bought them?
Answer: Each likely assumes the other (or another relative) brought them.
Jason HoffmanQuestion: How would the train have been able to go back the same way with the ice on the lake cracking?
Answer: Because it's a magic train.
Jason HoffmanQuestion: When the boy trips on the ball, what's the thing that it hits?
Answer: It looks like a hubcap.
Answer: The instrument is called a Hurdy-Gurdy. It is a type of wound string instrument.