Short answers, pulled from the story.
The French Directory began its executive power on the 26th of October 1795 when five men took their seats in the Luxembourg Palace. This followed the adoption of the Constitution of Year III by referendum on the 24th of September 1795.
Economic collapse occurred because assignats paper money fell to a fraction of their value while public revenues were nonexistent and citizens lost the habit of paying taxes. The government printed assignats based on confiscated property but could never keep pace with demand, causing prices for wine and flour to rise dramatically within months.
Napoleon Bonaparte received command of the Army of Italy on the 2nd of March 1796 through Barras influence. He defeated Sardinians at Mondovi on the 22nd of April 1796 and Austrians at Lodi on the 10th of May 1796 before forcing Emperor Francis II to sign the Treaty of Campo Formio in October 1797.
The coup began on the 4th of September 1797 when General Pierre Augereau arrived Paris with troops to arrest Pichegru and other royalist deputies after Barras discovered contacts between them and exiled monarch Louis XVIII. The Directory annulled elections of about two hundred deputies across fifty-three departments and deported sixty-five deputies to Guiana to secure its power.
Between the 4th of September 1797 and the end of the Directory in 1799, one hundred sixty persons were condemned to death by military tribunals including forty-one priests and several women. Seventeen Paris newspapers closed on the 17th of December 1797 while substantial taxes were imposed on all newspapers and magazines distributed through mail excluding Jacobin scientific art publications.
The French Directory ended when Bonaparte returned from Egypt on October 1799 to engage Abbé Sieyès in a parliamentary coup d'état on the 9th and the 10th of November 1799. This coup abolished the Directory and replaced it with the French Consulate led by Napoleon Bonaparte.