As you've indicated, the regiment was organic to 31st Infantry Division (the division was the principal component of the Alabama National Guard both prior to and subsequent to the war). Company E was an element of the regiment's 2d Battalion - one of the battalion's three rifle companies.
The regiment was constituted and organized in the Alabama State Militia in 1836 but I won't go that far back. Assigned to 31st Division in 1923, the entire division was inducted into Federal service in November 1940 and served in the Pacific Theater during the war. Decorations: Philippines Presidential Unit Citation. Campaign credits: New Guinea (Invasion), New Guinea (Campaign), Western Pacific (Invasion of Morotai, Halmahera Group), Western Pacific (Morotai), Southern Philippines, Philippines Liberation Streamer with one bronze service star. How any the above applies to your man depends on his dates of service with the regiment and other factors.