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If I have understood your question correctly, you want receive submission email after the form is submitted and also send a copy to the person who submitted the form. Is that correct?
To receive submission emails to your email address, you should add an notification email alert in your form. The following guide should help you: http://www.jotform.com/help/25-Setting-Up-Email-Notifications
You should also change the Recipient Email address of your form's notification email alert to any desired email address on which you want to receive the submission emails. The following guide should help you: http://www.jotform.com/help/41-Finding-out-E-mail-Address-used-for-submission-notifications
To send an email to the person who submitted the form, you should add an "Form Autoresponser" email alert in your form. The following guide should help you: http://www.jotform.com/help/26-Creating-a-Form-Autoresponder
I am not sure if I have understood your last part of your question "and for it to remain editable". Please explain your question a bit more in detail and we will surely help you.