Can't answer all of your questions but can give some info that may. Let me describe Capt. Water's Battery. Yes, it was part of the 2nd Alabama Artillery Battalion, being Company B. It was commanded by Captain David D Waters from its formation in December 1861. Lieut. C W Watkins filled in temporary for Waters in late fall, 1862 until spring 1863 guess why is Waters was recovering from wounds??? Waters resumed command in spring 1863 late fall 1863 replaced by Lieut. W P Hamilton late in 1863. The battery was destroyed at the Battle of Chattanooga and disbanded in January 1864. It was common for the confederate army to refer to batteries by the commanders names, Waters-Hamilton-Watkins and the official name Btry B, 2nd Alabama Art. Btn. So as you research, use all four designations to follow the battery. Yes, Isaiah Griffin most likely left Mobile in March 1862 and sent to Corinth MS with the battery. Problem was that Corinth was a unhealthy location because the water was bad. Sickness in the army was bad and the numbers grew. It is possible that Sergeant Griffin got sick in Corinth and was hospitalized in April, 1862. The illness may have been dysentry or a intestinal infection?? I did find that Isaiah Griffin was a sergeant when he went into the army and was a private in March 1863 when he was discharged. This is all I can provide so good luck with further research.
Ron