For the vast majority of people caffeine is very mild compared to cocaine. Coca leaves are in the ballpark of caffeine, however you would rate that subjectively. And personally I think I would have found it hard to tell which was which in a blind test.
As a side note coca tea (or chewed leaves) are often recommended for managing altitude, and chewing leaves did seem to help with headaches I was having at > 12k feet, but again it was fairly subtle, and I am not convinced it's not just placebo/a nice distraction.
No, Aumann's theorem proves a much more limited thing. For one thing, it assumes agents have a common prior, which is a very strong assumption not present in most cases where people "agree to disagree".
When the disagreement starts from foundational subjective disagreements, such as what constitutes malpractice or intent or incompetence, etc, the theorem has nothing to say, and it is perfectly reasonable to say that you "agree to disagree".
In this particular trial it wasn't used for treatment but for prevention, the patients don't have HIV (and none had it at the end of the trial either because it was so successful!)
That said: generally there's no guarantee of continued treatment.
It does in fact prevent infection you have misunderstood.
It very clearly prevents infection incredibly well, proof of that in the real world is exactly why there is excitement over this drug.
It also sounds as though you misunderstood the mechanism, it interferes in both an early and a late step in the viral process, there no theoretical reason to describe it as "not interfering with infection".
What is unique about Nicaraguan sign is that the entire process of evolving from a loose invented communication system with lots of pantomime and little regular linguistic structure into something with grammar and visual "phonemes" and a fixed core vocabulary was observed in real time over several generations of speakers.
As successive group of users were introduced to it as new native speakers they evolved it adding more and more structure, it doesn't start out fully language like at first. I can't think of any other case where that process has been documented in action.