If you want to get emails from a gmail account, and want a webhook to do such, you could use Context.io's Webhook Feature.
However, at the maximum volume you'll be able to send out with Gmail, I'd recommend looking toward an email service provider's free plan. If you're familiar with SendGrid already SendGrid's Free Plan will give you access to both low volume sending, and the Parse webhook. Other email service providers will give you the same functionality on their free plans, as well (e.g. Mailgun).
Disclaimer: I am a SendGrid employee.