Who established the first monastery?

Answer 1

Saint Kevin of Ireland.

Answer 2

The earliest known Christian monastic communities consisted of groups of cells built into mountainsides or huts collected around a common center, which was usually the house of some hermit or anchorite famous for his holiness or singular asceticism. In the earliest beginnings of Christian monasticism, the ascetics were accustomed to live singly, away from people in general, but not too far from a village church. Increasing religious zealotry, aided by persecution, drove them farther and farther away from the civilization into mountains or deserts. The deserts of Egypt swarmed with the "cells" or huts of these anchorites. Anthony the Great, who was a desert-dweller in A.D. 312, was the most celebrated among them for his austerities, his sanctity, and his power as an exorcist. His fame brought him a host of followers, imitating his asceticism in an attempt to imitate his sanctity. The deeper he withdrew into the wilderness, the more numerous his disciples became. They refused to be separated from him, and built their cells around that of their spiritual father. In this way, there arose the first monastic community, consisting of anchorites living each in his own little dwelling, united together under one superior, Anthony the Great.

Answer 3

First type of Monastery adhered to Benedictine Rule, established by St. Benedict in 529AD.

Answer 4

I'm pretty sure it was Saint Benedict.