Short answers, pulled from the story.
Emperor Ashoka sent missionaries to the Kashmira-Gandhara region in 268 BCE following the Third Buddhist council held in Pataliputra. Majjhantika, a monk from Varanasi, was assigned by Ashoka to preach in Kashmir and Gandhara during his reign which lasted from 268 to 233 BCE.
Phase II of Gandharan architecture spanned from the middle to late 1st century CE through early 3rd century CE. This period characterized expansions of Butkara I and Dharmarajika complex with addition of stupas, relic shrines and monasteries alongside narrative reliefs on the biography of the Buddha.
The Kushan Empire existed between 30 and 375 CE and provided crucial support for Buddhist religion throughout Gandhara. Kanishka the Great ruled from 128 to 151 CE while Huvishka succeeded him as ruler of the empire.
Mahayana Pure Land sutras were brought from Gandhara region to China as early as AD 147 through work of Lokakşema. The earliest translations show evidence having been translated directly from Gāndhārī language by this Kushan monk.
Buddhism eventually ceased to exist from region by approximately 1200 CE due to various factors combined including Muslim invasions of India. Religion started its decline after the invasion by Hephthalites also called White Hunes into Gandhara during the middle of the fifth century.