Natural intelligence has not been understood because if our brains were simple enough that we could understand them, we would be so simple we couldn't. This explains why it has not been reproduced.
>There is no repeatable experiment going from inorganic matter to self-aware, self-replicating life.
You can do the RNA world experiments in a lab, it would just take a lot of time and a lot of primordial soup, but eventually you would observe abiogenesis. I also don't see how abiogenesis and biology are relevant.
>capable of doing the impossible, e.g. predicting the weather with fidelity substantially into the future.
Thankfully this is not a measure of intelligence, since we can't do that either.