Short answers, pulled from the story.
The Army of the Potomac crossed the Rapidan River on the 4th of May 1864 to begin the battle. Fighting continued through the morning and afternoon of May 5, with Grant maneuvering south by the morning of May 7.
Lieutenant General Ulysses S. Grant commanded all Union armies while Major General George G. Meade led the Army of the Potomac directly in the field. President Abraham Lincoln had promoted Grant from the Western Theater in March 1864 to give him command of these forces.
Union casualties totaled 17,666 men including 2,246 killed, 12,037 wounded, and 3,383 captured or missing. Historian Gordon C. Rhea suggests the actual number may be higher than the official report due to a lieutenant lowering the count.
Dense second-growth forest made mounted cavalry fighting nearly impossible and obscured visibility for infantry units. The thick vegetation filled with smoke caused soldiers to fire at sounds rather than visual cues leading to friendly-fire incidents and diminished artillery effectiveness.
Confederate troops mistook Longstreet's mounted party for Union soldiers while they moved through the woods near the Orange Plank Road. This confusion resulted in crossfire that severely wounded Longstreet in his neck on May 5.