WP Term Family

Yes. Please install the WP Term Meta plugin.

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 family using the "wp-term-meta" plugin!
    'meta_query' => array( array(
        'key'   => 'family',
        'value' => 'private'
    ) )
) );

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

http://github.com/stuttter/wp-term-family/