Why and when was the hour divided into exactly 60 minutes (and not for example 70 or 80)?
It comes from the ancient Babylonian numeration system which had base 60. (The reason for the choice of such a base is simplicity of calculation: 60 is divisible by 2,3,4,5,6,10,12,15,20,30. Much more convenient than base 10, whose only justification is the number of fingers on both hands).
It was used mainly in astronomy (ancient people had little need in dividing an hour into smaller parts, and if necessary they used 1/2 or 1/4 of an hour). Then with the spread of clocks, it started to be used in daily life.