IQ tests are frequently biased. How biased will vary from test to test. Also, the data is can be misinterpreted by those unfamiliar with the tests procedures/results 1
70-80% comes from where? Nobody knows exactly what the "smart genes" are, and studies in twins show that variance between individuals in IQ is about 50%-60% genetic...or 40-50% environmental factors2A/2B
Even Haier has said that the fact that intelligence is in some way genetic just means that the factors that might influence those aspects of it would also need to be genetic. This can include things like nutrition and mental illness/stress, which are more prevalent among poorer communities.
Mostly from twin studies. This number (at least the ballpark figure) is essentially uncontested amongst researchers at this point (see e.g. [1]). However, this is the heritability of the variability of intelligence in adults. In children, that number is close to the one you cited. The rest of what you’ve said is essentially true: heritability is extremely complex and we’re only now getting the first few association studies in to ascertain which genomic loci are associated with changes [2].
See The Neuroscience of Intelligence by Richard Haier for an overview of the current consensus in intelligence research.