Yes, you should include your php file in functions.php in WordPress theme folder. In functions.php : require( 'your_php_file' ); And write :

<?php
    add_action( 'init', 'fetch_login_form');
    function fetch_login_form() {
        $user_email = $_POST['user_email'];
        // write condition based on Username or User email.
    }

Yes, you should include your php file in functions.php in WordPress theme folder. In functions.php : require( 'your_php_file' ); And write :

<?php
    add_action( 'init', 'fetch_login_form');
    function fetch_login_form() {
        $user_email = $_POST['user_email'];
        // write condition based on Username or User email.
    }

Password is autogenerated while we receive an email so you can stop send email and allow user to register directly. Follow this link : How to disable wordpress confirmation email for new users