Sending emails for completely free isn’t possible unless it’s with your own gmail, but even then it would not be on your own domain. Considering if someone allows you to send emails for free and for anybody else using their SMTP, the IP reputation would soon fall off a cliff as most likely it would be abused for sending spam emails.
As far as I know only Zoho has a free plan and most others are free trials, there’s simply no easy way of sending emails on your domain for free.
However, receiving emails on your domain is possible using Cloudflare Area 1 which is free and it routes email to your gmail.
If you paid $ for a custom domain, just buy a SMTP service if you do not want the entire hosting (which is very likley far lower than a quarter your domain price btw), whether you code on phone or whichever financial status you’re in is not in scope of discussion.
Both Amazon and Microsoft (And maybe even Google) offer free plans for email sending (Technically they are trials, but you can make them behave just like free tiers by settings budgets).
It is 100% possible to send emails on your domain for free, but just like every other free thing in existence, there are limits. In this case, it’s how many emails you can send.
Various email providers have free tiers. Sendgrid, SMTP2GO, Brevo, Postmark and Mailjet are a few examples which all let you send a small amount of email per day and per month with your own domain.
These are all “free forever” deals, so there is no time limit, but the number of messages you can send is limited and there may be some other restrictions.
The free offer can also be cancelled. Sparkpost, Mailgun and Mandrill all had free tiers before, but don’t have it anymore now.