Short answers, pulled from the story.
The Battle of Palmito Ranch was fought on the 12th and the 13th of May, 1865, on the banks of the Rio Grande east of Brownsville, Texas. It took place more than a month after Robert E. Lee's surrender at Appomattox Court House on the 9th of April, 1865.
Private John J. Williams of the 34th Indiana Infantry Regiment is believed to have been the last man killed during the Battle of Palmito Ranch, making him the likely final combat fatality of the American Civil War. In 1896, a pension dispute over the veterans of this battle was resolved when the assistant secretary to the commissioner of pensions legally ruled them the last Union casualties of the war.
Both Union and Confederate commanders at Brownsville knew Lee had surrendered, but Confederate General Edmund Kirby Smith had not yet surrendered the Trans-Mississippi Department. Historian Jerry Thompson concluded that Confederate Colonel John Ford was motivated by honor, the defense of his men's dignity, and the protection of a large quantity of cotton belonging to Richard King and Mifflin Kenedy stored in Brownsville.
Colonel Theodore H. Barrett of the 62nd United States Colored Infantry commanded the Union forces at Palmito Ranch. Barrett was thirty years old and had served as an army officer since 1862 without ever seeing combat before ordering the attack.
The Battle of Palmito Ranch was a Confederate victory. Colonel John Salmon Ford's forces drove the Union troops back toward Boca Chica, surrounding and capturing 50 men of the 34th Indiana's rearguard, 30 stragglers, and 20 dismounted cavalry in a bend of the Rio Grande.
Most historians consider Palmito Ranch the last formal land battle of the Civil War, though the designation is disputed. Some sources identify a skirmish at Hobdy's Bridge near Eufaula, Alabama, on the 19th of May, 1865, as the last action, and historian Richard Gardiner argued in 2013 that the Palmito Ranch engagement was a post-war encounter rather than a true battle. The battlefield was designated a National Historic Landmark in 1997.