Our genes give us priors to evade lions and pick berries. Humanity as cultural organism can reprogram us to more abstract tasks, but it takes easily 10-20 years of training and we are relatively inefficient in them compared to our original task.
But even then. I don't think current in-distribution learning is enough even if we scale it up. There must be something else. We are at least 3-5 Turing awards away from AGI, I think.
Or it could be a complete dead end, as has happened before. And nobody could tell until it was done; even those who were correctly skeptical were really just lucky that there wasn't a rabbit in that hat. Sometimes there's a rabbit.
The best you are likely going to get is robustness wrt different environments, but the environments have to come from the same Meta-Distribution. Invariant risk minimization is an interesting research area in that direction, there is for example an adversarial formulation that seems quite elegant. I have never tried this, but I can imagine it is tricky to get to converge.
Yes. Humans can learn to answer questions even when questions (test cases) don't come from the same distribution as the training set.
You need to have some amount of analytical capabilities. Analytic as the ability to form distinct and modular concepts from the input and form representations that can be composed together to generate instances that don't exist in the distribution. The low-level example of this ability could be blind source separation.