Normallly, the baby house geckos will eat insects such as gnats, and yes they can catch them, and baby crickets, i think they might eat some kind of plant, but i am not sure. do some research before...
House geckos love cockroaches, crickets are their second favorite.They also eat mealworms and silkworms/waxworms but, cut the heads off of the worms because they can bite through the geckos...