1st Level Page with No Children

To expand upon my comment:

Top-level page? (q.1)

global $post;
$x = get_ancestors( $post->ID, 'page' );
if( ! $x ) {
    // there are no ancestors, therefore this is a top-level page
}

Childless page? (q.2)

global $post;
$args = array(
    'post_parent' => $post->ID,
    'post_type' => 'page',
);
$x = get_children( $args );
if( ! $x ) {
    // there are no children
}

References

• get_ancestors()
• get_children()

NB — this assumes that you’re after WordPress’s pages. If you want a different post type, replace page in the code samples with your chose post type’s name.