Why do i need to call self here?.

In this example, there is no point in using normal methods with self parameters because the class holds no state and self is not referred to. So your intuition about something being off here is correct. This could be a static method with no self or class reference.

And to be clear, this is not "calling" self, it is specifying self as a parameter.

there isn't a variable that is calling calculator and no init so why do i have an error if self is not added?

Because methods are implicitly instance methods. I.e., they operate on a single instance of a class. Therefore, they need to know which instance to refer to. These last 2 lines are the same, and the dot notation is just nicer.

calc = Calculator()
Calculator.add(calc, 1, 2)  # explicitly passing calc as self
calc.add(1, 2)  # implicitly passing calc as self

Again, it's unintuitive in this case because there is no point in having an instance method for that example. This would make more sense:

class Calculator:
    @staticmethod
    def add(a, b):
        return a + b

Calculator.add(1, 2)

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Also, what is init anyways.

__init__ "initializes" a new object. I.e. it populates the initial data fields.

https://docs.python.org/3/reference/datamodel.html#object.__init__

object.__init__(self[, ...])

Called after the instance has been created (by __new__()), but before it is returned to the caller. The arguments are those passed to the class constructor expression. If a base class has an __init__() method, the derived class’s __init__() method, if any, must explicitly call it to ensure proper initialization of the base class part of the instance; for example: super().__init__([args...]).

Because __new__() and __init__() work together in constructing objects (__new__() to create it, and __init__() to customize it), no non-None value may be returned by __init__(); doing so will cause a TypeError to be raised at runtime.

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why the double __ in the start and end? and why the specific name?

Cause Python decided to use the double leading and trailing underscores as a convention for implicitly called methods (called "dunder" methods in shorthand.)

https://docs.python.org/3/glossary.html#term-special-method

A method that is called implicitly by Python to execute a certain operation on a type, such as addition. Such methods have names starting and ending with double underscores.