Giving Halsey authority over Lyster simply makes no sense. Halsey is a TF commander with dubious intel. As free as possible means exactly that, not 'throw away your airgroups because a TF commander wants you to'. Lysters orders would be to destroy the IJN carriers, not throw a figleaf to the...
Trying to work out why Lyster sacrificed his air groups, rather than wait a few hours and brutalise any located Japanese carriers safely. Just to make Halsey happy. Halsey isnt his boss. Oh, right, reasons :P
The attacks from Midway were anything but ineffectual as they keep disrupting the japanese. See Shattered Sword.
Knowing who is where, and with what, is rather fundamental.
2-carrier groups are what can be handled at this point in the war. KB was working as two pairs.
Wit no details on the carrier loads or tf locations, it is pretty impossible to work out wat is hapenning and why. In OTL a second strike on Midway was needed, why is only one needed here? The tf allocation is odd, the fleet should have broken down to pairs of carriers, not triples. Why is...
given the ability of the FAA to do evil things to you at night, Japanese losses seem light.
I agree that it would be sensible to define aircraft types and numbers (be careful here, there is a lot of divergence between carried and operational aircraft)
Regarding the analysis of a carrier battle, there are a few points.
The RN are not getting into a daytime fight unless cornered - why on earth would they??
The British have no real intrest in a Pacific battle, so its likely it would take place in the Singapore area. So lurk under land based...