Customize and save send form email template

Is there a way to setup and save the body of the email (different from the current generic one) to send the form each time?

You can actually modify the content of the email just like what you can do in a regular word processor, however, there is no way to save your modifications.

Just to add though, if you simply want to share your form, you can just copy your form's URL, then using your own email client, paste the URL in there and add your modifications. This way, you can just go back to your Sent folder and copy the previous layout.

Where-to-Find-My-Form-URL

I was going to ask the same question. There is no template option like the auto responder section?

Unfortunately, no such option. You may consider sending the form through an email account or through other email services like Mailchimp that offers email templates.