Short answers, pulled from the story.
The International Astronomical Union was founded on the 28th of July 1919 at the Constitutive Assembly of the International Research Council in Brussels, Belgium. Its head office is based in Paris, France, on the second floor of the Institut d'Astrophysique de Paris.
Benjamin Baillaud of France served as the first President of the International Astronomical Union from 1919 to 1922. Alfred Fowler of the United Kingdom served as the first General Secretary.
The seven founding member states were Belgium, Canada, France, Great Britain, Greece, Japan, and the United States. Italy and Mexico joined shortly afterward, and ten more nations joined by the end of the first General Assembly in Rome in 1922, bringing the total to nineteen countries.
The IAU maintains two dedicated working groups for naming: the Working Group for Planetary System Nomenclature handles naming conventions for planetary bodies and surface features, while the Working Group on Star Names catalogues and standardizes proper names for individual stars. The IAU is the recognized global authority for all such designations.
As of the 1st of August 2019, the IAU had 13,701 individual members from 102 countries and 82 national members representing professional astronomical communities worldwide. The membership spans 90 countries and territories, with individual members being professional astronomers at the PhD level and beyond.
The IAU General Assembly meets every three years since its first meeting in Rome in 1922, with the exception of the period between 1938 and 1948, which was skipped due to World War II. An Extraordinary General Assembly was also held in Warsaw, Poland, in September 1973 to mark the 500th anniversary of the birth of Nicolaus Copernicus.