Display CPT taxonomies as an archive page

You’re describing the default behaviour. Based on your code, you will have the following URLs:

If any of these URLs are returning a 404, you likely just need to flush your permalinks. This needs to be done once after registering a post type for the first time. Visiting the Settings > Permalinks page is sufficient to do this (you don’t even need to press save, unless you make a change on the page).

As for the templates to use:

You can see an explanation and visualisation of the template hierarchy here.

An important thing to remember is that the templates for these all need to use the same main loop as all other templates:

<?php 
if ( have_posts() ) : 
    while ( have_posts() ) : the_post(); 
        // Display post content
    endwhile; 
endif; 
?>

WordPress will automatically query the correct posts to be displayed by this loop, so you should not be using a custom WP_Query to query posts in these templates.