In their natural habitats tree squirrels eat a variety of foods including fungi, insects, bird eggs and young birds, pine nuts, and acorns, plus a wide variety of other seeds, nuts, dried corn, fruits, twigs, buds, bark, leaves, pine cones, roots, and mushrooms.ere is a general list of what squirrels eat -- but each species has its favorite menu. The average life span for a squirrel in the wild is 3-5 years. Their main predators are hawks, owls, cats, and predators of baby squirrels can include snakes, crows and other squirrels.