Auto-Responder Email: How to know if the email was successfully sent?

where can I see if the autoresponder email has been sent correctly to the submitter of the form? is there also any statistics about the autoresponder email?

If you're using our default sender email addresses then you should be able to find these auto-responders emails in the email history, here is a guide that will help you to check your email history: How-to-View-All-Your-Form-Email-History

You will find the emails sent to your email recipient address and you should find auto-responders emails, you should find using either your form ID or the submitter's email address. 

Hope this helps.