Short answers, pulled from the story.
The word pataphysics appeared for the first time on the 28th of April 1893 inside Alfred Jarry's play Guignol. It was published by the French newspaper L'Écho de Paris littéraire illustré while Jarry was only twenty years old.
Alfred Jarry defined pataphysics as the science of imaginary solutions that examines phenomena existing beyond standard reality. The concept functions as a parody of scientific method while pretending to be serious philosophy and attributes properties of objects to their virtual lineaments.
A society called the Collège de 'Pataphysique formed in Paris during 1948 with members committed to learned and inutilious research. The permanent head of the college is named Dr. Faustroll who is a fictional character created by Alfred Jarry.
Buenos Aires hosted one of the first pataphysical institutes outside France in the 1950s while London established its Institute of 'Pataphysics in September 2000. A separate institute opened in Vilnius Lithuania during May 2013 and local groups developed in Germany Sweden Switzerland Canada and The Netherlands between 1975 and 2000.
The pataphysical calendar started in 1949 when the Collège created it and each month contains twenty-nine days with two exceptions for imaginary dates. The 29th Gidouille falls on the 13th of July every year without exception and the 29th Gueules appears only during leap years on the 23rd of February.