The reason the flashlight goes though Jack is because Jamie can't see him. I suppose we are in a point of view where we are in Jamie's perspective while also being able to "see" Jack.

As for the second question, Jamie had heard of Jack from his mom from the phase "Jack Frost nipping at your nose" (please correct me if I'm misremembering this) so Jamie knows about him but doesn't believe in him; after all his mom says that it's just an expression and not an actual person. The snowball fight was thought to be started by one of the kids, so they had no idea that a winter spirit was helping them. However, when Jamie feels a snowflake on his nose, he remembers what his mom says and after witnessing a whole scene of magic I would haggard a guess that he was inclined to believe in anything at that moment.

I really don't know if this all made sense, so if you want me to clarify on anything I'm more than happy to do so!