At what point in the below points, assuming you trust the results and instruments etc, can you no longer discover causal relationships?

For the first three, clearly you can. The fourth is the tricky case. The difference between the third and the fourth is that in the third, the "someone" has already learned about causation, so when they read about what was done, it is as good as having done it themselves. At least, they will understand the causal relationships claimed, even if the paper does not contain enough detail for them to replicate it.

In the fourth case, the Armchairian (Scott Aa's name for them) has never interacted with the world, only watched it as if on a television screen or through a read-only internet connection. One can consider two different versions of the Armchairians, depending on whether they have the power to direct their gaze wherever they choose or not (or whether they have the power to type in URLs or not), but in either case it is not clear to me what the answer is.

To give a more concrete example than the parable of the Armchairians, which could be run as a practical causal analysis challenge, could a program whose only input was the Facebook firehose discover causal relationships in the data?