Hopefully someone with a better understanding of the test will come along and answer your question. I can, however, tell you what our psych told us- the FSIQ is *not* calculated by averaging the four scores. He said many parents get home and call him back saying "wait, I think you did the math wrong" so he always tries to provide parents with that info. Although I have no idea how FSIQ actually is calculated, I can say that the FSIQ your daughter got was likely correct. Hope that's at all helpful!
Yes, that's exactly right. The FSIQ (and GAI) are calculated looking at how rare it is to get scores of the sort the child did on all of the subtests, not just by averaging the subtests. So, for instance, it is less common to be high on everything than high in just one area so even a bunch of subtest scores where none of the subtests is quite in the gifted range could come together to produce a moderately gifted composite score b/c it is uncommon to be nearly gifted everywhere and, overall, that is enough to be gifted.
I hope that isn't just more convoluted! FWIW, the GAI would be even higher. You'd be looking at a 139 (99.5th percentile) for a GAI.