How to update feed only 2-3 times a week (for Feedburner email)?

You should be able to use this function to delay the RSS feed as long as you desire. (example, 48 hours or every two days)

// delay feed update
function publish_later_on_feed($where) {
    global $wpdb;

    if (is_feed()) {
        // timestamp in WP-format
        $now = gmdate('Y-m-d H:i:s');

        // value for wait; + device
        $wait="10"; // integer

        // http://dev.mysql.com/doc/refman/5.0/en/date-and-time-functions.html#function_timestampdiff
        $device="MINUTE"; // MINUTE, HOUR, DAY, WEEK, MONTH, YEAR

        // add SQL-sytax to default $where
        $where .= " AND TIMESTAMPDIFF($device, $wpdb->posts.post_date_gmt, '$now') > $wait ";
    }
    return $where;
}
add_filter('posts_where', 'publish_later_on_feed');

source: https://wordpress.stackexchange.com/a/1896/12086