Did babylonia have a powerful state with a large bureaucracy? what state services, now taken for granted in dealing with crimes, were absent in this society? why was so much attention given to issues of false accusation ?

Babylonia did indeed have a very powerful state with a large byrocratic apparatus. Babylonia did not have a police force, which is now taken for granted as a state service dealing with crimes. False accusations were taken very seriously, since the punishment for them was death. This was regulated by the Law Code of Hammurabi.