Question: What kind of instrument was the bum playing when we first meet him?
Answer: The instrument is called a Hurdy-Gurdy. It is a type of wound string instrument.
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.
Question: When Hero Boy gets back from the toy room in the train, what were all the kids shouting?
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.
Question: In the scene at the end where the conductor is finishing stamping everyone's ticket (e.g. know-it-all got 'learn', girl got 'lead', etc), what was on Hero Boy's ticket? I didn't watch the English version and the conductor said not to say it out loud.
Answer: It says "Believe".
Question: Why does Hero Boy imagine Lonely Boy?
Answer: Hero Boy isn't imagining Lonely Boy. He is a real character that interacts with Hero Boy, Hero Girl, the Conductor and the elves at the North Pole.
Question: 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.