Short answers, pulled from the story.
The Battle of Spotsylvania Court House took place from May 8 to the 21st of May 1864. The main fighting occurred during this period with intense combat continuing until around midnight on May 13.
Lt. Gen. Ulysses S. Grant served as commander of all Union armies while Maj. Gen. George G. Meade remained the actual commander of the Army of the Potomac. Union corps commanders included Warren's V Corps, Hancock's II Corps, and Sedgwick's VI Corps.
Grant ordered Meade to follow wherever Lee went with a strategy that accepted high casualties because the Union had far greater resources to replace lost soldiers and equipment. The goal was not a quick victory but a war of attrition designed to wear down Confederate manpower.
Lee lost another 10,13,000 men about 23% of his army while Grant lost close to 3,000 killed out of over 18,000 total casualties. Five general officers were killed or mortally wounded including Union Maj. Gen. John Sedgwick who famously said They could not hit an elephant at this distance shortly before his death.
Fighting at the Bloody Angle continued day and night until around 12:00 a.m. on May 13 at the base of the Mule Shoe defensive line. Bodies piled up four and five high and soldiers were forced to pause from time to time and throw corpses over the parapet since they formed an obstacle in the way of the fighting.