In the movie roman holiday with audrey hepburn there is a scene with a big sun statue? that has its mouth open and they stick their hand in it. Where is this statue? does it really exist?

Yes! The statue is known as the "Bocca della Verita" (mouth of truth) and it's outside a church in Rome called Santa Maria in Cosmedin, which you will find on any tourist map of Rome. There was a small queue to be photographed putting your hand in the mouth when I was there last. The church itself is small but lovely, with gorgeous "cosmati" work (inlay of marble/semi precious stone).