Generally speaking the barrels of a battleship's turrets can indeed be elevated and fired independently. Most navies' tactical doctrines during the World War II period, however, called for the guns to operate in salvoes under most circumstances.
All the turrets in the main battery (two turrets, in the case of the
Graf Spee normally would be controlled electronically by the main gun director, on top of the superstructure. (If the target was ahead or astern, obviously, only one turret could be brought to bear on it.) There are plenty of instances of guns firing individually for one reason or another (damage or mechanical problems, for instance), but under normal circumstances all the guns of the main battery that could be brought to bear on the target would fire at once.
Another point for model building purposes: the gun director controlling the turret that's firing should be pointed on the same bearing as the turret.
Hope this helps.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.