Short answers, pulled from the story.
The Battle of Stones River was fought from the 31st of December 1862 to the 2nd of January 1863, in Middle Tennessee. The Confederate army withdrew on the 3rd of January, and Union forces occupied Murfreesboro on the 5th of January.
Total casualties at Stones River were 25,645: 13,906 Union and 11,739 Confederate, representing 32.7% of all troops engaged. Of roughly 78,400 men who fought, 3.8% were killed, 19.8% wounded, and 7.9% missing or captured, giving Stones River the highest percentage of casualties of any major battle in the Civil War.
The Union Army of the Cumberland, commanded by Maj. Gen. William S. Rosecrans, won the battle after the Confederate Army of Tennessee under Gen. Braxton Bragg withdrew to Tullahoma, Tennessee on the 3rd of January 1863. The victory was costly but strategically significant, securing Nashville as a Union supply base and boosting Northern morale after the defeat at Fredericksburg.
President Abraham Lincoln wrote to Rosecrans that a defeat at Stones River would have been one "the nation could scarcely have lived over." The victory provided a critical morale boost after the Union's defeat at Fredericksburg and reinforced Lincoln's political foundation for issuing the Emancipation Proclamation, which discouraged European powers from intervening on the Confederacy's behalf.
Hell's Half-Acre was the soldiers' nickname for Round Forest, a rocky four-acre wooded area where Col. William B. Hazen's brigade held its position against repeated Confederate assaults on the 31st of December 1862. It was the only part of the original Union line that did not break. The Hazen Brigade Monument, erected there in May 1863, is the oldest intact Civil War monument in the United States.
Bragg withdrew beginning at 10:00 p.m. on the 3rd of January 1863 because he learned Rosecrans was receiving reinforcements rather than retreating, Confederate intelligence suggested Union forces would soon number 70,000 against his 20,000 available troops, and freezing rain risked raising the Stones River high enough to split his army. He retreated 36 miles south to Tullahoma, Tennessee.