Using HTTP Authentication

I am building a REST API in PHP to work with a JavaScript based app. All requests are handled as JSON and some requests require authentication.

An example request would be:

$.ajax({
    type: 'GET',
    url: 'http://domain.com/api/posts/recent.json',
    headers: {
        Authorization: 'X-TRUEREST ' + $.param({
            username: 'johndoe',
            password: '********'
        })
    },
    success: function(response){
            // Handle response here (includes auth errors too)
    },
    error: function(a,b,c) {

    }   
});

I have based the use of HTTP Authentication headers on the code in this plugin: https://github.com/kvz/cakephp-rest-plugin/blob/master/Controller/Component/RestComponent.php#L532

As you can see they take passed parameters with the header and then they are used to log a user into the system if they are not already. From what I can tell they expect the auth credentials to be passed WITH the request for data.

An example of this is (note not using CakePHP in my example app):

if ( $loggedIn ) { // logged in is true of false based on session existing

    // Then return the JSON as normal

} else {

    // Grab HEADERS INFO

    $headers = $_SERVER['HTTP_AUTHORIZATION'];
    $parts = explode(' ', $_SERVER['HTTP_AUTHORIZATION']);

    // Then use the parts to find a user in the DB... and populate $user

    if($user){

        $this->Auth->login($user); // login the user with our authentication code

        // Then return JSON as normal

    } else {
        print json_encode(array('auth'=>false))
    }

}

A few questions that I have though:

Question 1: Why use the HTTP Authentication and headers? As as far as I can tell, they are not offering me anything unless I am using t