The longest range in which a land-based artillery piece ever deliberately hit a target was a US Army 16-inch/45 coast defense gun which scored a hit at 35,200 yards (17.4 nautical miles) in August 1938 under what was described as "perfect conditions of weather and sea".
The longest range hit at sea happened on July 9, 1940 when the British battleship Warspite put a 15-inch round into the Italian battleship Giulio Cesare at 26,000 yards (12.8 nautical miles).
There were actually several battleship engagements in WWII
North Sea, April 9, 1940: KMS Scharnhorst and KMS Gneisenau fight an indecisive action with HMS Renown off Norway.
Mers El-Kebir, July 3, 1940: The HMS Resolution, HMS Valiant and HMS Hood bombard the French fleet near Oran, Algeria. Sinking the old battleship Bretagne, badly damaging her sister Provence and less seriously damaging the new Dunkerque while the latter's sister Strasbourg escaped unscathed.
Calabria, July 9, 1940: Another intense, but indecisive action is fought in between the Italian Giulio Cesare and Conte di Cavour vs. HMS Warspite, HMS Royal Sovereign and HMS Malaya.
Denmark Strait, May 24, 1941: KMS Bismarck and the heavy cruiser Prinz Eugen sink HMS Hood and badly damaging HMS Prince of Wales.
North Atlantic, May 27, 1941: HMS King George V and HMS Rodney get revenge for the sinking of Hood by reducing Bismarck to a shattered wreck.
Casablanca, November 8, 1942: USS Massachusetts exchanges gunfire with the partially competed French Jean Beat which is badly damaged.
The 2nd Naval Battle of Guadalcanal, November 14-15, 1942: HIJMS Kirishima vs. USS Washington and USS South Dakota. South Dakota was damaged and Kirishima was pounded so badly that she had to be scuttled the next morning.
North Cape, December 26, 1943: HMS Duke of York sinks KMS Scharnhorst in a protracted slugging match.
The Battle of Surigao Strait, October 24-25, 1944: A US squadron including USS Mississippi, USS Maryland, USS West Virginia, USS Tennessee, USS California and USS Pennsylvania (all but the Mississippi being veterans of Pearl Harbor) vs. HIJMS Fuso and HIJMS Yamashiro. The IJN was ambushed by the US battleships and thier escorts in an action that was so one-sided that Pennsylvania never got a chance to fire. This is the last battleship action in history.
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The reason that the American Army does so well in wartime, is that war is chaos, and the American Army practices chaos on a daily basis.
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