My general disagreements with those axioms from my reading of the literature are around the concepts of immutability and of the belief in the almost entirely biological factor, which I don't think is well supported by current research in genetics, but that may change in the future. I think primarily I disagree about the effect sizes and composition of factors with many who hold these beliefs.

I do agree with you in that I generally have an intuition that intelligence in humans is largely defined as a set of skills that often correlate, I think one of the main areas I differ in interpretation is in the interpretation of the strength of those correlations.

I think most in the rationality community (and otherwise in the know) would not say that IQ differences are almost entirely biological - I think they'd say they're about half genetic and half environmental, but that the environmental component is hard to pin to "parenting" or anything else specific. "Non-shared environment" is the usual term.

They'd agree it's largely stable over life, after whatever childhood environmental experiences shape that "non-shared environment" bit.

This is the current state of knowledge in the field as far as I know - IQ is about half genetic, and fairly immutable after adulthood. I think you'll find the current state of the field supports this.