Earlier quoted context omitted.
There is nothing smart about current LLMs. They just regurgitate text compressed in their memory based on probability. None of the LLMs currently have actual understanding of what you ask them to do and what they respond with.
If LLMs just regurgitate compressed text, they'd fail on any novel problem not in their training data. Yet, they routinely solve them, which means whatever's happening between input and output is more than retrieval, and calling it "not understanding" requires you to define understanding in a way that conveniently excludes everything except biological brains.
Yes, and that's exactly what they do.
No, none of the problems you gave to the LLM while toying around with them are in any way novel.