Extract url of every image in library?

First you have to get all attachments. You can use get_posts function for this:

$attachments = get_posts( array(
    'post_type' => 'attachment',
    'posts_per_page' => -1,
) );

Then you have to loop through them and get their urls using wp_get_attachment_url:

foreach ( $attachments as $att ) {
    echo wp_get_attachment_url( $att->ID );
}