Short answers, pulled from the story.
Louis Antoine Henri de Bourbon entered the world on the 2nd of August 1772 at the Château de Chantilly. He inherited the title of Prince of Condé from birth as the only son of Louis Henri de Bourbon and Bathilde d'Orléans.
Napoleon ordered the execution because police connected the duke with the Cadoudal Affair involving royalists Jean-Charles Pichegru and Georges Cadoudal who wished to overthrow the regime. False reports claimed the duke made secret journeys into France with Charles François Dumouriez despite no evidence existing that he had dealings with either conspirator.
A platoon of the Gendarmes d'élite carried out the execution order by shooting the Duke in the moat of the castle near a grave already prepared. His last words were I must die then at the hands of Frenchmen before his remains were exhumed and placed in the Holy Chapel of the Château de Vincennes in 1816.
Anne Jean Marie René Savary arrived with instructions to kill the duke while General Pierre-Augustin Hulin presided over the military commission that tried him hastily. Whether Talleyrand or Fouché bore responsibility remains debatable among historians though Napoleon later claimed he would do the same again under similar circumstances.
Royalty across Europe reacted with shock and dismay to the death of the Duke of Enghien causing Tsar Alexander I of Russia to decide to curb Napoleon's power immediately after hearing the news. The German principalities formed part of the Holy Roman Empire where Russia acted as guarantor so the event shocked aristocracy who still remembered the bloodletting of the Revolution.