That depends on which division you're referring to - there are several divisons in the US Army, US Army Reserve, and US Army National Guard. The rank typically held by a Division Commander is Major General (two stars).
The Army is composed of several divisions, which are further organized into corps. Which division did you have in mind?
ADC is usually the abbreviation for Assistant Division Commander. Other variations include ADC-M (Assistant Division Commander - Maneuver), ADC-S (Assistant Division Commander - Support), and ADCO (Assistant Division Commander for Operations).
No. Commander is a job title (e.g., Company Commander, Battalion Commander, Brigade Commander, Division Commander, Corps Commander, etc.), but not a rank. Lieutenant Commander and Commander exist as ranks only in the Navy. Lieutenant Commander is equivalent to a Major in the Army, Air Force, and Marines, and Commander is equivalent is Lieutenant Colonel in the Army, Air Force, and Marines.
George Gordon Meade was commander of the 3rd Division, I corps, Army of the Potomac
Henry Heth was a division commander in the Confederate Army of Northern Virginia.
He started in France in 1940 as the commander of the 7th Panzer Division and then went to North Africa as commander of the German Afrika Korps, then returned to France as commander of Army Group B
Major Generals are two star generals, and the normal position for them is commanding a division. The US had about 65 infantry divisions, 16 armored divisions, two cavalry divisions, five airborne divisions and one mountain division. A division commander took orders from his superior officers, a corp commander, and above him a field army commander, then a theater commander, and ultimately the Chief of Staff of the army, and the president. A major general commanding a division in WWII had three infantry regiments in an infantry division, or three "combat commands" in an armored division. He had to order these take objectives assigned to him by his superiors, using the best arrangements to get the job done with minimum loss. He had staff officers to help him run a division. A division had about 15,000 at full strength.
The army commander commanded the army. This was nominally the Pharoah. Sometimes he appointed an army commander to take to the field in his place.
No, there is no rank of commander in the Army. In the Army commander is a title, not a rank. In the Navy, there is a rank of Commander, it is the equivalent of Lt Colonel or O-5.
The main leader of D-Day in Europe was General Eisenhower. There where a few others who helped from the British forces. Obviously the above answer is from an American. Actually General Bernard Montgomery was the Ground Forces Commander in Chief (21st Army Group). The senior U.S. Commander was Lieutenant-General Omar Bradley Commander U.S. 1st Army (composed of the 1st U.S. Infantry Division, the 4th U.S. Infantry Division, the 29th U.S. Infantry Division, the 82nd U.S. Airborne Division and the 101st U.S. Airborne Division). while Lieutenant-General Mike Dempsey Commanded the 2nd British Army (composed of the 3rd British Infantry Division, the 6th British Airborne Division, the 50th British Infantry Division and the 3rd Canadian infantry Division under Major-General R.F.L. Keller)
A one star US Army General (Brigadier General-for Brigade Commander). A US Army brigade is authorized a full Colonel as commander; if the brigade is deployed alone (without a division), such as the 1st Brigade of the 5th Mechanized Infantry Division was in Vietnam (the only one to be deployed as such); then that brigade is authorized a General to command it; hence a Brigadier General.
A Corps is a body of men which is made up of 1 or more divisions. Army or Army Group is bigger, Division is smaller than a Corps. If you take D day as an example: Eisenhower is the Army commander. Bradley & Montgomery each command Army Groups, the people like Leese, Hodges & Patton are Corps Commanders.
General George Washington was commander of the Continental Army.