The Peacock tarantula, scientifically known as Poecilotheria metallica, is not an omnivorous crustacean. It is a carnivorous arachnid that primarily feeds on insects and other small invertebrates, making statement I incorrect. The species is indeed found in a limited habitat in India, specifically in a small area of less than 100 square kilometers in Andhra Pradesh, which makes statement II correct. Additionally, the Peacock tarantula is an arboreal species, meaning it lives in trees, which makes statement III correct. Therefore, the correct statements are II and III.