In your fpm.conf file you haven't set 2 variable which are only for error logging.
The variables are error_log
(file path of your error log file) and log_level
(error logging level).
; Error log file
; Note: the default prefix is /usr/local/php/var
; Default Value: log/php-fpm.log
error_log = log/php-fpm.log
; Log level
; Possible Values: alert, error, warning, notice, debug
; Default Value: notice
log_level = notice