LISP is as old as I am (1958), but its influence is still visible as more modern languages like Closure and Haskell are clearly influenced by it. Last time I used it, though, was on my Commodore 64 in the early '80's.
Learning LISP therefor is in my opinion very useful if you want to study functional languages but not very useful or productive in practice.
In that case it's younger than I am. I would suggest that Lisp, Forth and APL are outliers as far as general purpose programming languages are concerned and all of them were designed and implemented by people isolated from (and possibly ignorant of) the work that became ALGOL hence the vast majority of today's general-purpose languages.
However I broadly agree with your conclusion: it's worth having a nodding acquaintance with it as the foundation of an (outlying) branch of the language tree.
No, everything LISP is Turing complete, like Pascal, so it is possible to implement everything any language can do.
I respectfully suggest that you are perpetrating a misunderstanding. "Turing complete" means that a language can implement a Turing machine, and it's possible for a language to implement things that cannot be implemented by a Turing machine.
As a specific example, a Turing machine has a finite number of states, plus an infinite tape. Since the position of an infinite tape requires an infinite amount of state (bits, digits, etc.) to represent, the position of the tape cannot be represented in the control unit. Hence it is not possible to implement e.g. a recursive coroutine mechanism or interrupt handlers, since these require that the position of the tape be stored in the control unit.
The fact that those can be handled in Pascal suggests that Pascal is a superset of the Turing machine architecture. So while Lisp and Pascal might be Turing-equivalent, a Turing machine per se. isn't relevant.
Unfortunately, I've seen a lot of people holding forth on this in the past and using "Turing complete" to promote all sort of wild suppositions.
MarkMLl