Short answers, pulled from the story.
Buddhist monasticism was founded by Gautama Buddha during his own lifetime, between the fifth and fourth centuries BCE. He accepted a group of fellow renunciants as his first followers, establishing the order of monks and nuns.
The three surviving Vinaya traditions are Theravada, which governs monastic life in Sri Lanka and Southeast Asia; Dharmaguptaka, which governs East Asia; and Mulasarvastivada, which governs Tibet and the Himalayan region. Each maintains a separate ordination lineage.
The number varies by tradition. Theravada and Mulasarvastivada monks each observe approximately 258 rules, while Dharmaguptaka monks observe 250. Nuns follow more rules: 311 for Theravada, 348 for Dharmaguptaka, and 354 for Mulasarvastivada.
Mahaprajapati, the Buddha's stepmother, was the first woman to receive permission to live as an ordained practitioner, opening the bhikkhuni lineage. The Buddha's disciple Ananda argued strongly in favor of including a female order.
The Meiji-era Nikujiku Saitai Law declared that clergy of any Buddhist sect in Japan were free to marry. This was part of the broader Haibutsu kishaku movement, which promoted State Shinto and suppressed Buddhism as a foreign religion. The Vinaya ordination lineage had already become extinct in Japan, replaced by Bodhisattva vows that did not maintain the same celibacy requirements across all sects.
Following the 1959 Tibetan uprising, Chinese authorities forced thousands of monks to abandon monastic life and marry, converting them into ordinary citizens. Forced laicization occurred again during the Cultural Revolution, and monks who resisted were imprisoned, subjected to hard labor, tortured, or executed.