How are hereditary neural circuits created in the brain during early development?
This is one of the most important question in neurosciences and we are far from understanding it. This is also the topic of the entire subfield of neurodevelopment (to answer your last question).

First, you are right that the exquisite degree and physiological correspondence between individuals of a species, and even between species, indicate a strong genetic component. But you are also right that we have good evidence for a developmental component to brains physiology. Here are a few random examples (at the top of my head, so maybe not the most important/influential papers):


Cells selectivity in the primary visual cortex depends on visual experience. Animals housed in an environment with only horizontal or vertical stripes will have cells selective only to horizontal or vertical orientations (Blakemore &amp; Cooper, 1970).
At birth the primary visual cortex doesn't have cortical maps. They develop over time (e.g. Chapman, Stryker &amp; Bonhoeffer, 1993).
Due to synaptic pruning, newborn have actually more connections than later in life. These connections will be progressively eliminated during youth.
Inserting a third eye in the forehead region of frogs makes connections to their optic tectum and creates columns of ocular dominance just as their normal 2 eyes (Constantine-Paton &amp; Law, 1978). Even though having a 3rd eye is clearly not genetically encoded.
Similarly, rewiring the retinal projections of ferrets to their auditory cortex will form orientation columns just as in the primary visual cortex (Sharma, Angelucci &amp; Sur, 2000), even though this area usually processes a completely different modality.
Putting amblyopic (a developmental visual disorder) rodents in complete darkness for some time seems to "reboot" their visual system and cure them from amblyopia (He, Ray, Dennis &amp; Quinlan, 2007).
Efficient encoding of natural statistics mimics the response properties of cells in the nervous system (e.g. Olshausen &amp; Field, 1996).


What these different experiments suggest is that the overall structure of the brain is genetically determined, but development is truly what shapes the function and selectivity of cells.

Blakemore, C., &amp; Cooper, G. F. (1970). Development of the brain depends on the visual environment. Nature, 228(5270), 477-478.

Chapman, B., Stryker, M. P., &amp; Bonhoeffer, T. (1996). Development of orientation preference maps in ferret primary visual cortex. Journal of Neuroscience, 16(20), 6443-6453.

He, H. Y., Ray, B., Dennis, K., &amp; Quinlan, E. M. (2007). Experience-dependent recovery of vision following chronic deprivation amblyopia. Nature neuroscience, 10(9), 1134-1137.

Constantine-Paton, M., &amp; Law, M. I. (1978). Eye-specific termination bands in tecta of three-eyed frogs. Science, 202(4368), 639-641.

Sharma, J., Angelucci, A., &amp; Sur, M. (2000). Induction of visual orientation modules in auditory cortex. Nature, 404(6780), 841-847.

He, H. Y., Ray, B., Dennis, K., &amp; Quinlan, E. M. (2007). Experience-dependent recovery of vision following chronic deprivation amblyopia. Nature neuroscience, 10(9), 1134-1137.

Olshausen, B. A. (1996). Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 381(6583), 607-609.