Short answers, pulled from the story.
Promulgation is the formal proclamation that a new statutory or administrative law has been enacted after its final approval. In many jurisdictions it is a required step before a law can take effect, and it typically involves publication in an official government gazette or bulletin.
Promulgation is usually performed by a head of state: the president in countries such as France, Germany, India, Portugal, and Romania; the king or queen in Belgium, Spain, and the United Kingdom; the emperor in Japan; and the grand duke or duchess in Luxembourg. In Sweden, promulgation is performed by the Government rather than a single official.
It depends on the country. The emperor of Japan cannot refuse to promulgate a law. In France and Italy, the president may ask for reconsideration once but must ultimately promulgate if Parliament re-approves the legislation. Germany's president may refuse if the law is deemed evidently unconstitutional, though the threshold for that judgment is contested.
When the Indian Parliament is not in session, the president of India may promulgate an ordinance on the recommendation of the Union Cabinet; it carries the same force as an act of Parliament. The ordinance ceases to operate if Parliament does not approve it within six weeks of reassembly, or if both houses pass disapproving resolutions.
A law issued by the pope is promulgated when it is published in Acta Apostolicae Sedis, and by default takes effect three months after that publication. Canon 7 of the 1983 Code of Canon Law states the principle Lex instituitur cum promulgatur, a formulation traceable to the 12th century canon law codifier Gratian.
By ancient custom, acts of the Manx legislature Tynwald took effect only after being promulgated at an open-air sitting on Tynwald Hill at St John's, held on the 5th of July since the Gregorian calendar was adopted in 1753. Since 1988, only the short title and a summary of the long title are read aloud, and an act ceases to have effect if it is not promulgated within 18 months of royal assent being announced in Tynwald.