nginx / php / php-fpm | Problem with storing cookies
The various session cookie parameters are all documented here.
In particular, check the "session.use_cookies", "session.use_only_cookies", and "session.trans_sid" settings. If PHP can't succesfully create a cookie, it'll fall back to the trans_sid method (which is what you're seeeing: the session ID being passed around as a query/form variable).
You can trivially check if any cookie-related headers are going out by using Firebug and HTTPFox in Firefox. Both let you view the incoming/outgoing headers for requests.
May be some usefull information can be found in PHP-fpm error log? Set parameters in php.ini
error_reporting = E_ALL & ~E_DEPRECATEDlog_errors = Onerror_log = ;some file php can write in or "syslog"
Also try to look in nginx error log.
Does PHP-fpm process-owner has write permissions to sessions dir? See session.save_path on php.ini for session dir