No, not entirely. Most of the biplanes for example (like the Japanese were fighting in China and Manchuria, and the Finns in Russia) had lower wing loadings. As did the Hawk 75 (or roughly identical, apparently, to the Ki-43-I). The I-16 also had a very low wing-loading.
Anyway wing loading is just a function of wing area and weight so when we give you weight and wing area that is essentially your wing loading. Wing shape and engine power have something to do with turn rate as well but a lot of it is just that. The relevant exception here being the Ki-43 with it's additional maneuvering flaps giving it an extra boost in turn rate.
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The P-40 was also little to a lot (10-50 mph) faster than the F2A (depending on which exact types you are comparing and at what altitude) and had one of the best roll-rates of any fighter in the world, up around 100-130 degrees per second depending on the specific test, the variant, and the speed (P-40s rolled best at higher speed). F2A had a roll rate around 70-80 degrees per second though that would vary a lot depending on weight in the wings (like guns, fuel), speed, and possibly some other factors. P-40 also had a much higher dive speed of 460-480 mph depending on subtype, vs about 360 mph for the F2A (again, depending on the type).