Can an email be sent with each new form completion?

Yes. You can send a notification and an auto-responder when the form is submitted. If you are creating a new form and when the email field is added to the form, the notification and auto-responder will be created automatically. If you need add then manually, please refer to the guides below that can help you with this.

https://www.jotform.com/help/25-Setting-Up-Email-Notifications 

https://www.jotform.com/help/26-Creating-a-Form-Autoresponder 

Hope this information helps!