Short answers, pulled from the story.
The Vinaya is the body of monastic rules and ethical guidelines governing fully ordained monks and nuns in Buddhist communities. It forms one of the three main components of the Buddhist canon, alongside the Sutra and Abhidharma. The word derives from a Sanskrit verb meaning to lead, train, or guide, and is often translated as discipline.
The number varies by tradition. The Theravada tradition has 227 rules for monks and 311 for nuns. The Dharmaguptaka tradition, followed in East Asia, prescribes 250 rules for monks and 348 for nuns. The Mulasarvastivada tradition, followed in Tibetan Buddhism, sets 253 rules for monks and 364 for nuns.
The earliest dates scholars can establish for most Vinaya texts are the 5th-century Chinese translations. For the Theravada Vinaya, the earliest anchoring dates come from Buddhaghosa's 5th-century commentaries; manuscripts only reached Western scholars in the 17th and 18th centuries. The Mulasarvastivada Vinaya's earlier Sanskrit manuscripts date to the 5th through 7th centuries.
The three living Vinaya traditions are Theravada, used in Sri Lanka and Southeast Asia; Dharmaguptaka, used in China, Korea, Taiwan, and Vietnam; and Mulasarvastivada, used in Tibetan Buddhism and the Himalayan region. Five other Indian Buddhist Vinaya schools are preserved only in manuscript form and are no longer used for ordination.
Daoxuan (596-667) was the founder of the Southern Mountain School, or Nanshan lu zong, the dominant tradition of Vinaya interpretation in China. His authoritative commentary on the Four-Part Vinaya, compiled in 626, became the central text of the school. His influence was reinforced by support from the Tang imperial court.
The Tibetan Buddhist tradition of fully ordained bhikshuni nuns officially recommenced on the 23rd of June 2022, in Bhutan, when 144 women were ordained. The lineage had been lost after the persecution of Tibetan Buddhists by Udum Tsenpo following its initial transmission to Tibet by Shantarakshita.