Short answers, pulled from the story.
Chanakya used the word ānvīkśikī to mean critical inquiry within his text written during the 4th century BCE. This term distinguished itself from darśana which simply meant seeing or looking at truth.
The division depends on whether a school accepts the Vedas as valid knowledge. It also hinges on beliefs about Brahman, Atman, and the afterlife with exceptions like Mimamsa rejecting belief in an afterlife while Samkhya denies the premise of Brahman.
Parshvanatha led the Śramaņa order in the 9th century BCE according to historical records. He existed approximately 250 years before Mahavira who revitalized ancient teachings in the 6th century BCE.
Six major orthodox schools emerged including Nyaya, Vaisheshika, Samkhya, Yoga, Mīmānsā, and Vedanta for the orthodox group. The heterodox group contained Jain, Buddhist, Ajivika, Ajñana, and Charvaka traditions.
Charvaka embraced direct perception and empirical evidence while rejecting ritualism and supernaturalism. Primary literature like Barhaspatya sutras were lost either due to waning popularity or unknown reasons.