> Is immutability exclusive to functional programming?

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.

You don't need coroutines or async or anything complicated to model monads, just functions and data structures. Search for "c++ monads" and you'll find a ton of examples.