Short answers, pulled from the story.
The Battle of Bautzen was fought on the 20th and the 21st of May 1813 between Napoleon's French army and a combined Prusso-Russian force. Napoleon's 144,000 troops drove back the nearly 96,000 allied soldiers but failed to destroy them, primarily because Marshal Ney did not block the allied retreat as planned. The outcome is often described as a Pyrrhic victory for France.
Marshal Ney became confused and his faulty positioning on the first day left the allied army a gap to escape through. On the second day he grew distracted by seizing a village and lost focus on the strategic objective of cutting off the Prusso-Russian retreat, allowing the allies to withdraw when Tsar Alexander I ordered a general retreat at 4:00pm on the 21st of May.
The Prussian forces were led by General Gebhard Leberecht von Blücher and the Russians by General Peter Wittgenstein. Both generals had been ordered to stop retreating and make a stand at Bautzen by Tsar Alexander I and King Frederick William III following the allied defeat at Lützen.
Combined losses on both sides totaled around 20,000. Some sources, including Dr. Stubner, argue French casualties were significantly higher due to their aggressive attack tactics, while allied losses were between 11,000 and 14,000.
The Armistice of Pläswitz was signed on the 4th of June 1813, following an allied request on the 2nd of June. It was originally set to last until the 20th of July but was extended to the 10th of August. Napoleon later said on Saint Helena that agreeing to the truce was a serious mistake, because the nine-week pause benefited the allies more than the French, and when fighting resumed Austria had joined the coalition.
General Geraud Duroc was Napoleon's close friend and Grand Marshal of the Palace. He was mortally wounded by a cannonball the day after the Battle of Bautzen and died from his wounds.