WP Term Icons

No. There are no new database tables with this plugin.

No. All of WordPress’s core database tables remain untouched.

With WordPress’s get_terms() function, the same as usual, but with an additional meta_query argument according the WP_Meta_Query specification:
https://codex.wordpress.org/Class_Reference/WP_Meta_Query

$terms = get_terms( 'category', array(
    'depth'      => 1,
    'number'     => 100,
    'parent'     => 0,
    'hide_empty' => false,

    // Query by icon using the "wp-term-meta" plugin!
    'meta_query' => array( array(
        'key'   => 'icon',
        'value' => 'dashicons-networking'
    ) )
) );

The WordPress support forums: https://wordpress.org/support/plugin/wp-term-icons

The JJJ Software, Inc. page: https://jjj.software/wp-term-icons/