Short answers, pulled from the story.
The Mahāyāna Mahāparinirvānā Sūtra emerged in the second century CE within South India, specifically in regions like Andhra or the Deccan plateau. This era coincided with the rule of the Śātavāhana dynasty which provided significant patronage to Buddhist cave temples such as Karla and Ajañtā.
The core innovation of the Nirvana Sūtra lies in its redefinition of buddha-nature as an eternal pure self known as ātman. The sutra describes buddha-nature as a hidden treasury present in all living things without exception that can be revealed by removing negative mental afflictions.
The earliest known Chinese translation called the six fascicle text was produced between 416 and 418 CE by Faxian and Buddhabhadra during the Jin dynasty. Early catalogues attribute the work primarily to Buddhabhadra and his assistant Baoyun rather than Faxian.
Some passages depict icchantikas as scorched seeds unable to sprout while others suggest they possess buddha-nature and can eventually achieve Buddhahood if faith arises. Daosheng rejected the shorter translation for its exclusionary stance on icchantikas until Dharmakshema's new translation vindicated his position.
The Nirvana Sūtra profoundly shaped East Asian religious thought by inspiring the formation of the Nirvana School between 420 and 589 CE. Its teachings later merged into the Tiantai tradition under scholars like Pao-liang who died in 509 CE and influenced Japanese traditions such as Zen Nichiren and Shin Buddhism.