How to Convert Parent Page’s URL in Singular Name format when Child page is open

When registering your CPT, the rewrite and has_archive parameters will control the URLs (untested):

register_post_type( 'course', array(
    ...
    'rewrite' => array(
        'with_front' => false,
        'slug'       => 'course',
    ),
    'has_archive' => 'courses',
);