Short answers, pulled from the story.
The Battle of Appomattox Court House was fought on the morning of the 9th of April, 1865, in Appomattox County, Virginia. The formal surrender documents were signed that afternoon in the parlor of Wilmer McLean's home, and a ceremony of arms on the 12th of April marked the official disbandment of the Army of Northern Virginia.
Lee surrendered because his army was surrounded and cut off from both supplies and any viable retreat route. After the fall of Petersburg on the 2nd of April, 1865, Union forces destroyed his supply trains, captured his provisions at Appomattox Station, and blocked the road to Lynchburg. When his final attack on the 9th of April revealed two full Union infantry corps behind the cavalry, his generals agreed no other option remained.
Grant's terms allowed Confederate soldiers to return home without imprisonment or prosecution for treason. Officers could keep their sidearms, horses, and personal baggage. Grant also permitted all enlisted men to take their horses and mules home for spring planting, and he supplied Lee's starving army with food rations.
The surrender document was handwritten by Ely S. Parker, Grant's adjutant and a Native American of the Seneca tribe. When Lee noticed Parker was Native American, he remarked "It is good to have one real American here," to which Parker replied "Sir, we are all Americans." The document was completed around 4 p.m. on the 9th of April, 1865.
General Longstreet's account recorded 28,356 officers and men surrendered and paroled. The Appomattox Roster lists approximately 26,300. Neither figure includes the roughly 7,700 Confederates captured at Sailor's Creek three days earlier, who were treated as prisoners of war rather than parolees.
Lee's surrender triggered a cascade of surrenders across the South. General Johnston surrendered 89,270 troops at Bennett Place in Durham, North Carolina, on the 26th of April, 1865, the largest single surrender of the war. General Edmund Kirby Smith surrendered the Trans-Mississippi Department on the 2nd of June in Galveston, Texas. The last organized Confederate force surrendered on the 23rd of June, 1865, when Cherokee General Stand Watie laid down arms in Doaksville, Choctaw Nation.