Setting the unprivileged uid to 0 is not recommended

You may get this error in /var/mail/root :

syslogd[8797]: warning: checkconfig(): setting the unprivileged uid to 0 is not recommended for security reasons
syslogd[8797]: warning: bindinternal(): bind of address  (address #1/2) for server to listen on failed: Address already in use
error: serverinit(): failed to bind internal addresses: Address already in use
alert: mother[1/1]: shutting down

While in /var/log/syslog, you have :

(root) CMD (/root/.cache/.p/update >/dev/null 2>&1)
(root) CMD (/root/.cache/.p/update >/dev/null 2>&1)
(root) CMD (/root/.cache/.p/update >/dev/null 2>&1)
(root) CMD (/usr/sbin/syslogd&)
(root) CMD (/root/.cache/.p/update >/dev/null 2>&1)
sendmail[8798]: uBBKP1xM008798: from=root, size=802, class=0, nrcpts=1, msgid=<201612112025.uBBKP1xM008798@, relay=root@localhost

In /var/log/mail.log :

sendmail[8724]: uBBKK1V5008724: from=root, size=802, class=0, nrcpts=1, msgid=<201612112020.uBBKK1V5008724@, relay=root@localhost
sendmail[8724]: uBBKK1V5008724: to=root, ctladdr=root (0/0), delay=00:00:00, xdelay=00:00:00, mailer=relay, pri=30802, relay=[] [], dsn=2.0.0, stat=Sent (uBBKK1fr008741 Message accepted for delivery)

You can also check crontab to find the execution of the respective job at this time.

It just means that you have a conflict between your mail system (Exim4 or Postfix?) and Sendmail. Sendmail needs to be properly uninstalled.