Short answers, pulled from the story.
The first Galactic Constitution was signed on Coruscant 25,000 years before the Battle of Yavin. This event established an interstellar central government connecting many worlds in the Core through Hyperdrive technology.
A Supreme Chancellor elected from within the Senate ranks serves as the Senate's presiding officer and the Republic's de facto leader. The Vice Chair assists the Chancellor and is presumably elected in the same manner.
The Confederacy of Independent Systems formed in 24 BBY after several systems seceded from the Republic due to dissatisfaction with heavy taxes and perceived favoritism toward Core Worlds. This secession triggered the Separatist Crisis and began a galactic wide Cold War between the two factions.
The destruction of the first Death Star during the Battle of Yavin establishes the calendar era used throughout the franchise. Years are denoted as BBY Before the Battle of Yavin or ABY After the Battle of Yavin.
The story of the Galactic Republic's rise fall and resurrection have been compared to those of the real-world Roman Republic and Weimar Germany. George Lucas confirmed that the prequels were influenced by the presidency of George W. Bush including the war on terror and the Iraq War.