Short answers, pulled from the story.
The National Convention convened for its first session on the 20th of September 1792 inside the Salle des Cent-Suisses. This hall was small and cramped compared to the massive Salle des Machines where deputies would later meet from May 1793 onward.
Three major political factions dominated the National Convention throughout its three-year existence: The Montagnards, the Girondins, and the Plain. The Montagnards formed the biggest faction with approximately 302 to 309 deputies who sat on high bleachers earning them the name Mountain.
The Convention declared a French Republic unanimously on the 21st of September 1792 leaving the fate of Louis XVI unresolved. A commission examined evidence against him while the Legislation Committee considered legal aspects of any future trial.
A proclamation issued in Cap Francais on the 21st of June 1793 freed all slaves agreeing to fight for the French Republic from internal and external threats. The committee ruled that the Republic would pay indemnity to owners of female slaves marrying free men while all children of such unions remained free.
This marked the end of the National Convention which had sat from September 1792 through October 1795 under the adopted calendar system. A new constitution ushered in the French Directory on the 26th of October 1795 after Robespierre's fall.