display 1 post per author

Review and the following info and see if it points in the right direction:
https://wordpress.stackexchange.com/questions/63060/display-all-authors-and-their-only-one-latest-post

https://stackoverflow.com/questions/22436775/show-latest-post-from-each-author-if-post-is-not-older-than-a-month

@t-p thanks, I tried these, they do not work

The first example t-p linked uses outdated args. You could check you error log for suggestions on corrections. To save you the effort, use these args:

$args = array(
                    'posts_per_page' => 1,
                    'author' => $author['id'],
                    'ignore_sticky_posts' => 1,
              );
$query = new WP_Query($args);