May one go see a movie that is about christianity, like Mel Gibson’s new movie, especially if one considers it to be only entertainment? What about reading the New Testament out of curiosity when one knows its false?

I am sure you can find more productive uses for your time than giving your money to a producer whose work will encourage anti-semitism. It is permitted to read what the Christians call the New Testament if it is part of your studies of world history and culture and serves a positive purpose- like refuting the claims of the Christians. You should consult a rabbi who knows you personally.