Is `Object` a function in JavaScript?

You seem to be confused between "object" (the data structure) and Object (the function).

An object is a concept in JavaScript that is a generic container for some data. An object contains properties with keys and associated values.

In JavaScript, everything that is not a primitive is an object. This includes functions, which are basically a special type of object that can be "called" with the () syntax.

JavaScript provides a number of built-in functions that have various purposes. Two such functions happen to be called Object and Function. So in other words Object is a function and thus also an "object" (data structure).

Let's take your function Foo as an example:

function Foo() {
    var a = "3";
}

Foo is a function. This means that Foo can be called, eg. var f = Foo(). In this case f will be undefined since Foo doesn't return anything.

Because Foo is a function, it is also an object. This means we can also add and read properties from it:

Foo.bar = 5;
Foo.bar++;
console.log(Foo.bar); // prints 6

Please note that this "object" part of Foo is not related to the contents of the function. That means that the code you declared (var a = "3") is irrelevant. You cannot access var a in any way here because it does not exist until you call the function. If you were to do Foo.a, you are not manipulating var a inside the function; you are working with the property a on the object Foo.

You can however do it the other way around and access properties on Foo inside of the function:

function Foo() {
    var a = "3"; // a is local to this scope, you cannot get to it from outside
    console.log(a); // prints 3 - local variable a is accessible inside the scope of this function
    console.log(Foo.a); // prints 5 - a is a property on object Foo, and is accessible here
}
// var a inside Foo cannot be accessed here
Foo.a = 5;
Foo();

Edit: Re. your question regarding "this" in the comments. this is a special keyword in JavaScript that refers to an object. However, this object is not the function itself, it is a new object that is created when you call a function using the new keyword:

function Bar() {
    this.a = 10;
    console.log(this == Bar); // prints false
}
var bar = new Bar();
console.log(bar.a); // prints 10

A function that is meant to be called with the new keyword is referred to as a "constructor function". Object and Function are both examples of constructor functions, which is why their names start with an uppercase letter (a convention in JavaScript).

When you create an object with a constructor function, the property prototype of this function is used as the prototype (accessible through __proto__) of the created object.

console.log(bar.constructor == Bar) // prints true
console.log(bar.__proto__ == Bar.prototype) // prints true

this is also used for other things, but that is a broad subject and way out of scope for this question.

Function and Object are both constructor functions which can be used to create a function and an object, respectively, which is the reason typeof Function returns function.

About how functions and objects are related in javascript, consider the following points:

1. All non-primitive types are objects in JavaScript.
2. All objects directly or indirectly inherit from Object.prototype (unless prototype is changed explicitly using setPrototypeOf).
3. All native functions inherit from Function.prototype which inherits from Object.prototype, so it means function indirectly inherits from Object.prototype because functions are treated as objects in JavaScript.
4. The reason functions are treated as objects is because they can be passed as parameters to other functions and can be returned from functions i.e. higher order functions(a powerful feature of javascript).

5. A function can be called using the () operator because the JavaScript engine knows it is declared using a function keyword and has executable code. So whenever it is called, the JavaScript engine creates a new execution context and set the this binding and then executes the function. None of that happens when you try to call an object instead an error is thrown i.e. "is not a function".

   So we can say that not every object is a function because they may have not been declared using the function keyword and not have executable code.

6. As the function is treated as an object in JavaScript, we can add properties to it, create new objects from it.
7. A non-function type object cannot be called using () because it does not have executable code and is not declared using the function keyword. Instead, it is declared using new Object() or object notation and contains methods and properties.

I hope it clears both questions.

Q1: Why are they pointing to Function?

A1: Because they are functions. Function and Object are just constructor functions.

function is a Function object. object is an Object object.

Q2: If everything is an object in JavaScript, then why is Object a function?

A2: Because Object is just a constructor function.

typeof Object
// 'function'
typeof new Object()
// 'object'

And a function is an instance of Function, so that makes a function an object.

(function(){}) instanceof Function
// true

Fundamentally

Functions has some code that can be executed.
Object are those which contains data.

For class Point having x and y.

class Point {
    constructor(x, y) {
        this.x = x;
        this.y = y;
    }
    isOrigin() { return x == 0 && y == 0; }
}
let p = new Point();

Answer 1

In this, p is object which contains data or other functions.

p.isOrigin is function.

Similarly, class Point is itself a function which when runs produces p. That's why all classes like Object and Functions are functions more precisely constructor functions.

Answer 2

If everything is an object in JavaScript, then why is Object a function?

Same as Answer 1.

Also, how is a function actually implemented inside JavaScript?

Different JavaScript engines will have different implementations. They have specifications which they need to follow.

What happens to the variables declared inside a function?

Off topic. Every function runs with a scope which holds all data for that functions.

Is a function converted into an object by the JavaScript compiler?

Not sure what are you asking.