Short answers, pulled from the story.
The Lokottaravāda was an early Buddhist school that emerged as a subgroup of the Mahāsāṃghika, according to Mahāyāna doxological sources compiled by Bhāviveka, Vinitadeva and others. Its name comes from the Sanskrit lokottara, meaning supramundane or transcendent, referring to the teachings its followers upheld.
The Lokottaravāda traced its origins to the Ekavyāvahārikas and the Kukkuṭikas, according to the Śāriputraparipṛcchā and the Samayabhedoparacanaćakra. While the broader Mahāsāṃghika movement began around Magadha, the Lokottaravādins are known to have flourished in Northwest India.
The Mahāvastu is a biography of the Buddha that attributes itself to the Lokottaravādins and survives as a rare Mahāsāṃghika text preserved in its original Sanskrit. It appears to form an extended part of the school's Vinaya, and its Sanskrit text survived in the libraries of Mahāyāna Buddhists in Nepal.
Archaeologists rediscovered a Lokottaravāda vihara at Bamyan, in modern Afghanistan, that the Chinese monk Xuanzang had visited in the 7th century. Birch bark and palm-leaf manuscripts from the site, including Mahāyāna sūtras such as the Diamond Sūtra, are now held in the Schøyen Collection.
The Lokottaravāda held that the Buddha was lokottara, or transcendent, with his life and physical body treated as mere appearance rather than literal reality. Vasumitra's Samayabhedoparacanaćakra credits this view with qualities such as a limitless body, limitless power, and the ability to know all dharmas in a single moment of mind.
The Mahāvastu states that the future buddha Maitreya will be just one of a thousand buddhas destined to follow Gautama Buddha. This contrasts with the Theravāda, which holds that only five buddhas are destined to follow Gautama.