Short answers, pulled from the story.
The Italian Republic began on the 26th of January 1802 when the Consulta of the Cisalpine Republic received Napoleon Bonaparte in Milan. This event marked the constitutional transition from the Cisalpine Republic to the new state.
Napoleon Bonaparte served as president for ten years with full executive powers while Francesco Melzi d'Eril acted as vice-president during his absence. Melzi effectively ruled domestic affairs over the republic's three-year life before facing demotion when monarchy arrived.
Milan served as the capital city for this short-lived republic which covered primarily Lombardy and Romagna. The population reached 3,840,000 people across twelve departments including Milan which held 124,000 inhabitants according to records from 1764.
The state divided into twelve départements following the French system with an office created on the 6th of May 1802 designating prefects as department chiefs. These departments persisted within the new administrative framework even after the territory transformed into the Kingdom of Italy in 1805.
Napoleon assumed the title of Emperor of the French in 1805 causing the Italian Republic to transform into the Kingdom of Italy. This transition marked the end of the republican experiment in northern Italy while Napoleon became king and his stepson Eugène de Beauharnais served as viceroy.