Short answers, pulled from the story.
The word divan traces its lineage back to the Sumerian dub, a clay tablet used for record-keeping. This linguistic thread connects the ancient scribes of Mesopotamia to the grand viziers of the Ottoman Empire, showing how the concept of written administration survived millennia of cultural shifts.
The first true dīwān emerged under Caliph Umar in the year 636 CE, or possibly 641 CE, creating a registry of warriors from Medina who participated in the early Muslim conquests. This initial army register, known as the dīwān al-jund, was designed to facilitate the payment of salaries and rations to soldiers based on their service and their relationship to the Prophet Muhammad.
Caliph Abd al-Malik initiated a radical standardization of the government departments, replacing local languages and traditional book-keeping practices with a unified Arabic system. The process of Arabization was gradual and implemented region by region, with Iraq seeing the transition under Salih ibn Abd al-Rahman in 697, Syria under Sulayman ibn Sa'd al-Khushani in 700, and Egypt under Abdallah ibn Abd al-Malik in 706.
Caliph al-Mahdi created a parallel control bureau, the dīwān al-zimām, for every existing dīwān, acting as comptrollers and coordinators between the various bureaus. These control bureaus were essential for maintaining order and preventing corruption within the sprawling bureaucracy.
After 1565, administrative authority in Tripoli was vested in a Pasha directly appointed by the Sultan in Constantinople. The sultan provided the pasha with a corps of Janissaries, which was in turn divided into a number of companies under the command of a junior officer or Bey, and the Janissaries quickly became the dominant force in Ottoman Libya.