Asahi

CT

if only asahi in fleet and not flag ==> no CT bonus, no surface ship malus, no SS bonus
if only asahi flag ==> surface ship malus of ~0.63, SS bonus of ~1.365
if another CT flagship and asahi anywhere in fleet ==> CT bonus applies AND counts asahi as CT [with slightly higher modifier than expected], no surface ship malus, SS bonus of ~1.38, stacking multiplicatively with CT bonus
if asahi flag and another CT anywhere in fleet ==> CT bonus applies AND counts asahi as CT [with slightly higher modifier than expected], no surface ship malus, SS bonus of ~1.38
if asahi and another CT anywhere in fleet, but neither flag ==> CT bonus applies BUT doesn't count asahi as CT, nos urfact ship malus, no SS bonus
asahi sub bonus difference between with another CT and without shows no difference whether asahi is level 1-9 or level 10-29

so it seems CT bonus is katori-class intrinsic, but counts all CTs via class type :TanakaW~1: 🚬

conclusion can't be drawn for the following points:

3CT setups? [seems slightly higher than expected, but almost neglectible, missing data points for most exp ranges, might be possible to be explained with minuscle asahi bonus for CT bonus]
asahi and another CT in fleet, neither as flag [in particular: is asahi sub bonus active if no CT flagship, but still another in fleet]

asahi AR preliminary test results: [tests conducted with lvl 37 asahi kai and lvl 81 akashi kai, equipped with 3/4 repair cranes respectively]

if one AR is flagship and the other AR second ship in fleet, the whole fleet gets repaired, no matter whether asahi or akashi is flag (i.e. slot 6 doesn't get ignored if asahi is flag because of insufficient cranes on her)
both combinations CANNOT repair chuuha ships
both combinations still need 20 minutes before the first repair
both combinations reduce base repair time by multiplying time with ~0.85 (0.845 < x < 0.855) [confirmed for DD/CL, other ship classes still pending verification]

not checked yet: