I agree that the PCA's actions at Island No. 10 and New Madrid, etc. are the most confusing of any of their time at war. I haven't really studied it hard yet but it will take more time to figure out where they were at particular times.
As far as Batchelor's age, we are not talking about 1861. We are talking about April 1862. April 1862 minus August 1846 is four month shy of 16. I have a few who were younger than 16 and plenty age 16 when they signed up who were 14 when the war started. One 16 year old drowned in the Miss. River on the way to Belmont on a steamer. One was supposedly 12 when he signed up. He stuffed his boots with newspapers and stuffed his stomach with bannans to meet the height and weight requirement. He became a driver. One 15 year old came down from Kentucky with $200 to be shipped off to Scotland for education and to avoid the war, saw the PCA march through New Orleans on their way to Belmont, ran off from his daddy, bought two mules for the PCA with his education money and cut a deal with Bouanchaud himself the use of his servant to be allowed to join the unit. There is one well documented account from a lady in Alabama (about Spring of 1864) where she talks about how much the guys were gentlemen and they mention to her they have a "boy" in their unit who does as much work and is as brave as anyone else in battle. At that time there were several 16 year old thus a "boy" would be considerably younger. The "boy" could not have been the earlier mentioned 12 year old because he was out of the unit by then.
As far as Ive getting a pension after the war, I found this comment about him after the war. "He then became a planter, owning 1265 acres with 900 acres in cultivation, with 11 houses and lots in Bessemer, AL." I think I am correct that you had to qualify to obtain a pension. Wealthy people didn't qualify.
Regarding him being in school in 1863, that's not inconsistent in any way with what he was doing in '62. In fact, that he is not mentioned in school in '62 is consistent with him being up north then.
The account from Mrs. Bell Bushnell, pin pointing "Ives Batchelor" as the Union storming party took the flag from is compelling evidence. I mean, you can look everywhere in the United States in the 1860s and be hard pressed to find anyone named Iverson "Ive" Batchelor, and our Ive was from Pointe Coupee. Then there is an account of her actually interviewing him where he tells her about the flag and even who made it.
Union officer Johnston didn't storm the upper battery but he was in charge of the entire event and they gave him the flag. I have several first hand accounts of battles, etc. where they never mention quite a bit of carnage and deaths, but that doesn't mean it didn't happen. I say they wanted Johnston to keep the flag and thus didn't mention it. Maybe when the report was written they didn't know a flag had been captured. Bushnell was very high to do, living in New York, inteligent and revered that flag to the point of writing one book about it not to mention her other books.
As far as Ive possibly being discharged at age 16, it is very possible that his parents yanked him out of service. I have one account of a father writing the officers saying his 16 year old son did not have permission and that his mother was "very distrought" of something like that.
I don't see anything inconsistent with the given facts.