Agreed on the A/A - it was a negligible quantity.
Re - scout planes. Nagumo had plenty, (IJN doctrine called for up to 10% of carrier aircraft being used for scouting, meaning two dozen) Nagumo' staff just chose to use them for attack instead. His choice.
Re - presence of battleships. That's a fuzzier question, because if Yamato is present then Yamamoto's staff will be in the loop for the drama of the morning of the 4th. First off, Nagumo cannot countermand his standing order to maintain a naval reserve at 0715 because Yamamoto is right there, meaning that the armaments crisis cannot occur. Second, Yamaguchi's recommendation signals are being read in realtime by Nagumo's commander, meaning that Yamaguchi's suggestions may be ordered by Yamamoto to be implemented.
The Main Body of the Midway attack force under Yamamoto's direct command was there to be used in the classical way, the IJN always had been training for, the battleship vs battleship (or in the case of the Miodway operation: the remaining USN surface ships). For this reason, teh Yamato was accompanied by the other two largest battleships of the IJN, which would not have been needed, if the Combined Fleet had not expected to use them the way they had been constrcuted for in the first place, thereby saving fuel and resources.