Filter out comments with certain meta key/s in the admin backend

1. You can use pre_get_comments hook:

add_action('pre_get_comments', function($query)
{
    global $pagenow;
    if ( is_admin() && ('your-custom-page' === $pagenow) ) {
        $query->query_vars['meta_query'] = [
            'relation' => 'AND',
            [
                'key' => 'key1',
                'value' => 'meta1'
            ],
            [
                'key' => 'key2',
                'value' => 'meta2'
            ]
        ];
    }
});

2. You need to learn how to create an admin list table.

Also, take a look at:

• class-wp-comment-list-table.php
• edit-comments.php
• comment.php