A free alternative for listening to the webhooks might be a cloud function. I think you can get 2 million free function executions per month on Firebase. Or 125,000/month on Netlify (uses AWS Lambda).
For the emails, if you already use Mailchimp, then I think the Mandrill add-on might still offer 20,000 free transactional emails per month
Edit: Mandrill isn’t free at all, so Mailgun or SES might be the cheapest options. It looks like Mailgun currently is $0.80 per 1,000 emails and SES is $0.10 per 1,000 emails.