Short answers, pulled from the story.
Napoleon I distributed the eagle standards on the 5th of December 1804, three days after his coronation. This event was depicted in The Distribution of the Eagle Standards, an 1810 painting by Jacques-Louis David.
The original design was sculpted by Antoine-Denis Chaudet and copies were cast in the workshop of Pierre-Philippe Thomire. These bronze sculptures featured an eagle on a plinth with one claw resting on Jupiter's spindle.
The first capture likely occurred during the Battle of Austerlitz in 1805 when Russian cavalry under Grand Duke Konstantin overran the French 4th Régiment d'Infanterie de Ligne. The eagle was not recovered despite Napoleon winning the battle.
King Louis XVIII ordered all existing eagles to be destroyed as part of a decree reflecting the political shift toward royal restoration. Many eagles vanished during this period either melted down for their metal or hidden away to avoid destruction.
Eagles made during the Hundred Days in 1815 had closed beaks and were set in a more crouched posture compared to the originals. The workmanship was of lesser quality and these new models lacked the distinction of earlier versions.