Human language is unsuitable for "glass clear", unambiguous definitions, just because of its inherent fuzziness (which is nota bene an essential property for efficient communication).
No.
Prolog et. al. is based on Horn Clause representation and evaluated using something called SLD resolution.
"Concatinative" languages (like Joy) are based on function composition (not application.)
(FWIW, the Turing machine is not based on Lambda calculus. Not that TMs are a programming language.)
I sometimes wonder about the possible form of the "Platonic Ideal" is that each of these systems represent. George Spencer-Brown's Laws of Form seems to me to be the ultimate concrete example, but that's not a universally held opinion. :)
It's like Roman numerals vs. base-10 numerals, eh? "XXIII" and "23" both denote the same number (which may or may not exist depending on your metaphysical outlook) but neither notation can be said to be "the" notation.
Not really. FP has an obvious connection to lambda calculus. Many OOP languages don't even have a straightforward notion of "function", which is what lambda calculus is all about.
> There is a well-established theory of functions, the λ-calculus, ... However, our theory of objects is self-contained; it is the first that does not require explicit reference to functions or procedures.
So that answers your question in the negative and proves my point: no, not every language is based on lambda calculus.
See e.g. Landin, P. J. (1965): A Correspondence between ALGOL 60 and Church's Lambda-notation.