Two ‘If Statements’ is my syntax correct (functions.php) and what is ‘false’

You should use elseif for the second if statement:

$title1 = single_term_title( 'Conferences In ', false );
$title2 = single_term_title( 'CConferences In ', false );

add_filter( 'get_the_archive_title', 'my_theme_archive_title' );
function my_theme_archive_title( $title ) {
    if ( is_tax('us_state') ) {
        $title1;
    }
    elseif ( is_tax('country') ) {
        $title2;
    }
    else {
return $title;
}
}

You can read here about true/false https://developer.wordpress.org/reference/functions/single_term_title/