When you use SMTP as the Mailer Type in XI, it doesn't use Postfix to send email, it send it directly to the SNMP server and the messages in /var/log/maillog will not have any information on the Notifications from Nagios.
Q1. So see if a Notification was sent, you would look in the XI GUI and see that a notification was sent.
Then if there was an error, you would see in in the /usr/local/nagiosxi/tmp/phpmailer.log file. Only errors will be here, no logs if it was sent correctly.
Q2. If you want to use the xi_host_notification_handler, you will have to create a user account in the XI interface. That handler will use the email settings for the user account and not the Contact.
Take a look at this document for more details.
https://assets.nagios.com/downloads/nag ... ios-XI.pdf
Q3. Those messages can be ignored for the most part. They are probably messages sent from the cron daemon but you would have to see what they are for sure.