Seeing as I'm new, I might not know much, but if time moves so slow in the Tesseract, it might not have been a long conflict. Presumably, Schala and a Lavos Spawn (Which it seems to be, because of size issues, and being in the Tesseract doesn't change the whole DEAD thing) had a fight not with fists or magic, but with WILL. You don't need to be a god to have good willpower. And if Kid is truly a clone of Schala, then she has a lot of it ^^ Of course, Kid is a seperate entity entirely, so that might not mean jack squat. Regardless, it's probably safe to assume that the two confronted, started to biologically merge while their minds fought, Schala released Kid, and within seconds, Serge and crew come to her rescue.
As for this whole Arbiter thing, yea, that may be true. It could also be that her innate, strong magical power was required, and Queen Zeal just couldn't fill those shoes.