Two quick questions...can you chain 2 Emergency to X powers x2 together (I assume a cooldown between each)? IE EPTS II + delay + EPTW II + delay + EPTS I + delay +EPTW I + repeat
Yup, that works.
My second question is for AUX 2 SIF III...which skills boosts its effectiveness the most?
Like most ability's skills*, all 3 boost it in the same manner. 10 skill levels gained from raising 1 skill has the same impact as 10 gained from raising one (or both) of the other two. As such, you could say that the highest tier skill will raise it the most, since at 9/9, it provides the highest total of skill levels. But, from a gain per skill point system, it'll most likely wind up being a mix of the three.
* the exceptions are things like photonic fleet, where various skills impact abilities used by the ships summoned by the ability. So they could almost be described as a bundle of a couple abilities, rather than exceptions.