Not explicitly, I think no. But in some sense, yes. Arguably any tech which we don't really understand is a black box. I think the lack of understanding how something works is a large part of the "magical" effect.
Could you explain what you mean here? To the best of my knowledge, there hasn't been much success in successfully explaining how LLMs actually work? Of course we know all the low level mathematical details, we built them. But my understanding is that we don't really know much about the structure of LLM parameters and how they relate to the concepts the model is supposedly learning.
Nice, one would expect so. Though if you think more deeply about it, I think not. The language itself is the manifestation of capabilities, but the process exhibiting them is the underlying system, eg. neural nets or human brain.