How can you determine that email is actually sent or not from the Salesforce?

There is an Email log that you could use. It’s available in the setup menu under Monitoring.

It’s only for the past 30 days and you would have to manually check it.

From the email log page: “Email logs describe all emails sent through salesforce.com and can be used to help identify the status of an email delivery. Email logs are CSV files that provide information such as the email address of each email sender and its recipient, the date and time each email was sent, and any error code associated with each email. Logs are only available for the past 30 days.”