3 of 4 added 540 characters in body

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, 0 );

Reference