Short answers, pulled from the story.
The Dharmaguptaka sect was the first to establish Buddhism in Central Asia. According to scholar A. K. Warder, they executed a vast circling movement along trade routes from northwestern India into Iran and Oddiyana, then followed the Silk Road eastward into China, effectively establishing Buddhism there in the second and third centuries AD.
Greek artists in the Greco-Bactrian and Indo-Greek kingdoms created the first anthropomorphic representations of the Buddha, departing from the earlier aniconic tradition. Their images incorporated Greek stylistic elements including the himation robe, the contrapposto stance, curly hair derived from the style of the Belvedere Apollo (330 BCE), and the marble-and-mixed-material sculpting technique.
Khotan was one of the earliest Buddhist states in the world and served as a cultural bridge transmitting Buddhist culture and learning from India to China. By the time the monk Faxian visited, the entire population was Buddhist and the Gomati monastery alone housed 3000 monks. By the late 9th and early 10th century, Khotan had approximately 400 temples.
An Shigao, active roughly from 148 to 180 CE, was an Iranian Buddhist monk and the earliest known translator of Indian Buddhist texts into Chinese. By tradition he was a prince of Parthia who renounced his claim to the royal throne to serve as a missionary monk in China, earning the nickname the "Parthian Marquess."
Balkh fell under Muslim rule in 663, but the Nava Vihara monastery continued to function for at least another century. The Persian scholar Abu Rayhan al-Biruni reported that around the start of the 10th century the monasteries of Bactria, including Nava Vihara, were still standing and decorated with Buddha frescoes. Its hereditary administrators, the Barmakids, converted to Islam and became powerful viziers under the Abbasid caliphs.
Buddhism in modern Central Asia is practiced by small minorities. Uzbekistan's Buddhist population is 0.11 percent, concentrated among the Koryo-saram Korean minority, with one functioning temple called Jaeunsa in Tashkent. Kyrgyzstan has the highest percentage of Buddhists in the region due to historical Tibetan, Mongol, and Manchurian influence, with a registered community called Chamsen founded in 1996.