Is Unix an acronym?

Unix is not an acronym; it is a pun on “Multics”. Multics is a large multi-user operating system that was being developed at Bell Labs shortly before Unix was created in the early ’70s.

What is an acronym within an acronym?

Recursive acronyms typically form backwardly: either an existing ordinary acronym is given a new explanation of what the letters stand for, or a name is turned into an acronym by giving the letters an explanation of what they stand for, in each case with the first letter standing recursively for the whole acronym.