Short answers, pulled from the story.
The Battle of Stones River took place from the 31st of December 1862 to the 2nd of January 1863. The main fighting occurred on the first two days with a final Confederate withdrawal occurring on the evening of January 3.
Union Maj. Gen. William S. Rosecrans commanded the Army of the Cumberland during the battle. His force numbered about 43,000 men when it arrived near Murfreesboro on the evening of December 29.
Total casualties in the Battle of Stones River numbered 25,645 with 13,906 on the Union side and 11,739 for the Confederates. This represented 32.7% of all troops engaged making it the highest percentage of casualties of any major Civil War battle.
The battle was fought near Murfreesboro Tennessee where opposing armies bivouacked only two miles apart. Confederate forces withdrew through Murfreesboro on the evening of January 3 retreating to Tullahoma which is 36 miles south.
Bragg decided to withdraw his army on January 3 because false information planted by McCook made him believe Rosecrans was receiving reinforcements. The deception combined with heavy losses from attacks like the one at McFadden Ford led to the decision to retreat to Tullahoma.