Short answers, pulled from the story.
The Mulasarvastivada was one of the early Buddhist schools of India, which developed during the 2nd century CE and went into decline there by the 7th century. Its monastic code, the Mulasarvastivada Vinaya, is one of only three surviving Vinaya lineages in Buddhism, alongside the Dharmaguptaka and Theravada. The school's ordination lineage continues today in Tibetan and Mongolian Buddhism.
The relationship between the Mulasarvastivada and the Sarvastivada remains a matter of scholarly dispute, with modern researchers leaning toward classifying them as independent schools. Theories range from Frauwallner's view that the Mulasarvastivada was an independent community in Mathura, to Enomoto's claim that the two schools were really the same. No single theory has been definitively established.
The Mulasarvastivada spread throughout Central Asia through missionary activity, and the 7th-century monk Yijing recorded its prominence in Srivijaya (modern Sumatra, Indonesia) and Champa. Kukai, founder of the Shingon lineage in Japan, also required his students to study the Mulasarvastivada Vinaya.
On the 23rd of June 2022, 144 women were ordained as bhiksuni nuns in Bhutan, marking the official commencement of the Tibetan Buddhist bhiksuni tradition within the Mulasarvastivada lineage. Prior to this, Mulasarvastivadin bhiksuni ordinations had only been administered in Taiwan and later in Bodh Gaya, India.
The Mulasarvastivada Vinaya survives in a Tibetan translation from the 9th century, a Chinese translation from the 8th century, and partially in the original Sanskrit.
The Tibetan Emperor Ralpachen restricted Buddhist ordination exclusively to the Mulasarvastivadin Vinaya. As Buddhism later spread from Tibet to Mongolia, the Mongolian Buddhist tradition inherited this requirement and follows Mulasarvastivadin ordination rules as well.