Can I trigger a form from a Square purchase?

This is what I'm trying to do...

1. Buyer purchases a service online through their website (a Square.com feature on a WP site)

2. Purchase triggers the 1st form to be sent via email.

Do I use a Zap to do that? Or do I have to use the Square Jotform functionality to trigger that email to be sent. Or...?

You can integrate your form with Square and use it to create products for purchase.

When the form is submitted and the transaction has been completed a notification email would be sent to you and you can also setup the form to send an email to the form user.

https://www.jotform.com/help/459-How-to-Integrate-Form-with-Square

However, I'm not sure its possible with your requirements. Although it is possible to add the form link in the email.