Short answers, pulled from the story.
It was not a single army but three separate Confederate States Army formations that each carried the same name at different times. This name is distinct from the Union's Army of the Mississippi, which was named for the Mississippi River rather than the state.
The first Army of Mississippi was organized on the 5th of March 1862 under General P.G.T. Beauregard. It was renamed the Army of Tennessee on the 20th of November 1862.
General Albert Sidney Johnston commanded the army at Shiloh, taking charge on the 29th of March 1862 and leading it into the battle. He was killed in action on the 6th of April 1862, and General P.G.T. Beauregard resumed command that same day.
The second Army of Mississippi existed solely to defend Vicksburg, Mississippi, on the Mississippi River. After a long Union offensive and siege, Lieutenant General John C. Pemberton surrendered the army to Major General Ulysses S. Grant on the 4th of July 1863, opening the river to Union control and splitting the Confederacy in two.
The third Army of Mississippi was retitled III Corps, Army of Tennessee, around the 4th of May 1864, though it continued using its old name. Its last recorded commander was Major General William W. Loring, who served from the 14th of June to the 4th of July 1864.
The Confederate Army of Mississippi was named for the state of Mississippi, while the Union's Army of the Mississippi was named for the Mississippi River. The two names referred to entirely different forces operating in the same war.