Do I need to instantiate the XMLRPC class or any class in another class to access its methods?

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So far as I know, the XML RPC class is not instantiated unless needed, which is when the request is to /xmlrpc.php.

You would instantiate the class the same way the Core does:

include_once(ABSPATH . 'wp-admin/includes/admin.php');
include_once(ABSPATH . WPINC . '/class-IXR.php');
include_once(ABSPATH . WPINC . '/class-wp-xmlrpc-server.php');

/**
  * Posts submitted via the XML-RPC interface get that title
  * @name post_default_title
  * @var string
  */
$post_default_title = "";

/**
  * Filter the class used for handling XML-RPC requests.
  *
  * @since 3.1.0
  * @param string The name of the XML-RPC server class.
  */
$wp_xmlrpc_server_class = apply_filters( 'wp_xmlrpc_server_class', 'wp_xmlrpc_server' );
$wp_xmlrpc_server = new $wp_xmlrpc_server_class;

You have two options for doing that:

  1. Create a method inside your class to instantiate the XML RPC class,
    and save the instance to a class variable.
  2. Instantiate outside of the class and pass the instance to your
    class. This is something called “dependency injection“, which has both pros and cons.