WordPress – Custom Comments – Parent / Nested Reply

I am making a custom WordPress theme and have edited comments.php, but I’m unable to get the comments to save as a reply to another comment. I have succeeded in showing the comment parent id to show as a hidden value in the source code, but it doesn’t save it accordingly in the database (instead, it always saves the comment_parent as 0). Also, the commenter IP address isn’t saved either for some reason (comment_author_IP appears as “::1”). Here’s the code I have so far:

    <?php
    if ( post_password_required() )
        return;
?>

    <div id="comments" class="comments-area">

    <?php // You can start editing here -- including this comment!

    $fields = array(
    'author'               => '<p class="comment-form-author"><label for="author">' . __( 'Name', 'domainreference' ) . '</label> ' . ( $req ? '<span class="required">*</span>' : '' ) . '<input id="author" name="author" type="text" value="' . esc_attr( $commenter['comment_author'] ) . '" size="30"' . $aria_req . ' /></p>',
    'email'                => '<p class="comment-form-email"><label for="email">' . __( 'Email', 'domainreference' ) . '</label> ' . ( $req ? '<span class="required">*</span>' : '' ) . '<input id="email" name="email" type="text" value="' . esc_attr(  $commenter['comment_author_email'] ) . '" size="30"' . $aria_req . ' /></p>'
    );

    $defaults = array(
    'fields'               => apply_filters( 'comment_form_default_fields', $fields ),
    'comment_field'        => '<p class="comment-form-comment"><label for="comment">' . _x( 'Comment', 'noun' ) . '</label><textarea id="comment" name="comment" cols="45" rows="8" aria-required="true"></textarea></p><p class="comment-form-math"><label for="math">' . __( 'five plus two', 'domainreference' ) . '</label> ' . ( $req ? '<span class="required">*</span>' : '' ) . '<input id="math" name="math" type="text" value="' . esc_attr( $commenter['math'] ) . '" size="30"' . $aria_req . ' /></p></p><input type='hidden' name='comment_post_ID' value='' id='comment_post_ID' /><input type='hidden' name='comment_parent' id='comment_parent' value=''.$comment_parent.'' />',
    'must_log_in'          => '<p class="must-log-in">' .  sprintf( __( 'You must be <a href="%s">logged in</a> to post a comment.' ), wp_login_url( apply_filters( 'the_permalink', get_permalink( ) ) ) ) . '</p>',
    'logged_in_as'         => '<p class="logged-in-as">' . sprintf( __( 'Logged in as <a href="%1$s">%2$s</a>. <a href="%3$s" title="Log out of this account">Log out?</a>' ), admin_url( 'profile.php' ), $user_identity, wp_logout_url( apply_filters( 'the_permalink', get_permalink( ) ) ) ) . '</p>',
    'comment_notes_before' => '<p class="comment-notes">' . __( 'Your email address will not be published. Required fields are marked *' ) . ( $req ? $required_text : '' ) . '</p>',
    'comment_notes_after'  => '',
    'id_submit'            => 'submit',
    'title_reply'          => __( 'Leave a Reply' ),
    'title_reply_to'       => __( 'Leave a Reply to %s' ),
    'comment_form_title'       => __( 'Leave a Reply', 'Leave a Reply to %s' ),
    'cancel_reply_link'    => __( 'Cancel reply' ),
    'label_submit'         => __( 'Post Comment' )
    );

    comment_form($defaults);
    ?>

</div><!-- #comments .comments-area -->