Near the end, when the captain is walking out of the labyrinth holding the baby, you can tell it's a dummy. The baby does not move in the slightest, you can't even see it breathe.
The faun is not actually Pan. The film's correct title translated into English is 'The Labyrinth of the Faun'. However, the director, Guillermo del Toro, thought that the English-speaking audiences would get confused between a 'faun' (mythological creature) and a 'fawn' (baby deer). Therefore, for all English-speaking countries, the title is 'Pan's Labyrinth'.