Short answers, pulled from the story.
The War of the Third Coalition began in August 1805 when Napoleon shifted his army to the Rhine. The conflict concluded with the Treaty of Pressburg signed on the 26th of December 1805 which removed Austria from the war.
Napoleon led France while Austria sent Archduke Charles and General Mack to command their armies. Russia contributed forces under General Mikhail Kutuzov who fought alongside Austrian troops against French marshals like Masséna and Soult.
The Battle of Austerlitz occurred on the Pratzen Heights near Brünn on the 1st of December 1805. This location served as the centerpiece for the decisive engagement where Napoleon defeated the Allied forces.
Francis II abdicated the Imperial throne in 1806 causing the Holy Roman Empire to cease to exist. Napoleon created the Confederation of the Rhine shortly before this dissolution to replace the old empire structure.
Napoleon mustered approximately 75,000 men and 157 guns for the battle on the 1st of December 1805. The Allies fielded about 73,000 soldiers with seventy percent being Russian and 318 guns.