Short answers, pulled from the story.
The schism resulted from a dispute over the Vinaya, the Buddhist monastic code. A minority of senior monks called Sthaviras sought to add new rules to make the Vinaya more rigorous, but the majority of the Sangha refused. The Mahāsāṃghika Śāriputraparipṛcchā, the earliest surviving account of this event, places the decisive council at Pāṭaliputra.
The Mahāsāṃghikas held that the Buddha was supramundane (lokottara), with a limitless body, limitless power, and limitless lifespan. He never slept, never dreamed, and was always in samādhi. The historical Gautama was, in their view, merely one transformation body (nirmāṇakāya); the essential Buddha was identified with the Dharmakāya, the body of the teaching itself.
The Mahāsāṃghika sects originated in Magadha and spread to Mathura, Karli, Vārāṇasī, Pāṭaliputra, Kośala, Andhra, and Gandhāra. Their Caitika branch established major centers at Amarāvati and Nāgārjunakoṇḍā in the Coastal Andhra region. The cave temples at Ajaṇṭā, Ellora, and Karla are directly associated with the Mahāsāṃghikas.
The Mahāvastu is the most celebrated text of the Lokottaravāda branch of the Mahāsāṃghika school; its Sanskrit name means "Great Event" or "Great Story." It serves as a preface to the Lokottaravāda Vinaya Piṭaka and contains Jātaka and Avadāna tales about the past lives of the Buddha and other bodhisattvas. Scholars regard it as a primary source for the Mahāsāṃghika doctrine of the transcendent Buddha.
A. K. Warder has argued that Mahāyāna teachings clearly originated in the Mahāsāṃghika branch of Buddhism. The Aṣṭasāhasrikā Prajñāpāramitā Sūtra, estimated by Edward Conze to date to around 100 BCE, is linked by scholars to the Caitika subsect of the southern Mahāsāṃghikas along the Kṛṣṇa River in Āndhra. By the 7th century, Xuanzang and Yijing found that former Mahāsāṃghika territories were described as Mahāyāna.
The Mahāsāṃghika Vinaya was translated into Chinese between 416 and 418 CE by Faxian and Buddhabhadra at the Daochang Monastery in Nanjing, capital of the Eastern Jin Dynasty. The completed translation ran to 40 fascicles. Faxian had originally obtained the manuscript in Pāṭaliputra, where the Mahāsāṃghika Vinaya was reputed to be "the most correct and complete."