yes, but I believe we are using different interpretations fairness. as someone already pointed out, for fairness to be innate to humans it would need to be a better genetic trait compared to unfairness. so we are not arguing about how and if it is a good behavioural strategy, as it needs to be a better gene to have vs 'the-unfairness-gene'. so you might be genetically unfair and act fair as long as it is a valid behavioural strategy and revert to your genetic inclination when the situation requires you to (in case of serious danger for example). based on that it would be also possible to say that people are genetically fair and act unfair when in need, but that would not be fairness in my opinion.

Yes, TIT-FOR-TAT is the winning strategy in iterated Prisoners' Dilemma.

Basically, start off nice. If people are mean, punish them by getting mean. If they are nice, treat them in kind.