Short answers, pulled from the story.
Mahīśāsaka is one of the early Buddhist schools according to some records, believed to have originated in Mahishmati in the Avanti region of India. Its founder was a monk named Purāṇa, venerated in the Mahīśāsaka Vinaya preserved in the Chinese Buddhist canon.
The Mahīśāsaka sect was founded by a monk named Purāṇa and originated in Mahishmati, in the Avanti region of India. Purāṇa is venerated at length in the Mahīśāsaka Vinaya, a text preserved in the Chinese Buddhist canon.
Mahīśāsaka monks wore blue robes, according to two Chinese translations: the Da Biqiu Sanqian Weiyi, translated by An Shigao between 148 and 170 CE, and the Śāriputrapariprcchā. The Śāriputrapariprcchā states that the Mahīśāsaka school practiced dhyāna, penetrated deeply, and wore blue robes.
The pilgrim Xuanzang recorded that Asaṅga, an important Yogācāra master and the elder brother of Vasubandhu, received ordination into the Mahīśāsaka sect. The scholar André Bareau wrote that Asaṅga incorporated Mahīśāsaka doctrinal opinions into his later Mahāyāna Abhidharma work.
The Mahīśāsaka sect held that women could not become buddhas, and that five obstacles, including becoming a Cakravartin, a Māra king, a Śakra king, a Brahma king, or a Buddha, stood before them. This view is challenged in the Nāgadatta Sūtra, where the bhikṣuṇī Nāgadatta rejects the demon Māra's argument that she should settle for arhatship instead.
The Mahīśāsaka sect spread from Mahishmati in the Avanti region to Kashmir, to southern India including Nāgārjunakoṇḍā, and as far as Sri Lanka. In the 7th century CE, Yijing recorded the Mahīśāsaka, along with the Dharmaguptaka and Kāśyapīya, in parts of Oḍḍiyāna, the Kingdom of Khotan, and Kucha.