You can Feed them live crickets or any appropriate size insect. Unless it a large mantis use crickets the size of the mantises head or smaller. mist the enclosure a few times a day but dont saturate it to give it water. Feed as much as it will eat once a day.
Never kept any native ones but I would assume around 4-5 inches. When their small you can keep them in those little plastic critter cages you can get in pet stores, a large one I would use a 5-10 gallon tank with a tight fitting screen. for substrate you can use repti-bark.