No, but immutable defaults are powerful.
E.g. in JavaScript / Python, the built-in lists and dictionarys (which are blessed with special syntax) are mutable.
> Is the ability to use data/values exclusive to functional programming?
No, but expression-orientation makes this less painful
> Are monads exclusive to functional programming?
You can hack them in by abusing co-routines or perhaps async/await in various languages, but it will never be as good as something built for this purpose.
Type-inferences, type-classes and do-notation make monads workable in practice.