I see in filters.php "add_action( 'wp_head', 'rest_output_link_wp_head', 10, 0 )" Which makes me think this should do the trick to remove rel='https://api.w.org/'.
remove_action( 'wp_head', 'rest_output_link_wp_head' );
The rest... * cough * seem to be in default-filters.php
remove_action( 'wp_head', 'wp_oembed_add_discovery_links' );
To remove the rest_output_link_header
remove_action( 'template_redirect', 'rest_output_link_header', 11 );
Reference
