What is the use or what is the reason for new() and delete() to be implemented as operators in c++ ? What are the advantages of making it an operator instead of a function?
The new operator cannot be a function because it accepts a type as an argument. You cannot write new foo_type as a function call, because foo_type is not an expression that produces a value, but a type name.
The delete operator could be a function that is overloaded for different pointer types, and an extra optional bool argument for delete [] semantics. Why there is a delete operator is probably for symmetry with its new counterpart.
That said, template functions can take types as template arguments. But the new and delete operators historically precede templates.
Also, a function can be written which takes, instead of a type, a prototype instance of a type, from which an object is constructed: newobj(m_class(constructor_arg)). This newobj is overloaded for different types. It allocates space, copy constructs into it, and returns the object.
So in the end, the design reflects the tastes and whims of the designer.
The separation itself between operators and functions (and statements, declarations, and so on) is not strictly necessary in language design.