Added note to #3 to clarify MX Records cannot point to a CNAME or Alias but there is a work around discussed in this commit where you can create a second A record for subdomain.domain.tld and refer it to the IP address of your incoming mail server.
Added one additional bullet point under "Troubleshooting" section based on my experience implementing emailwiz with a New Top-level Domain (NTLD) and sending emails to colleagues at large F500 companies.
Technically Postfix is responsible for sending *and* receiving mail between *your server and other SMTP servers* (Mail Transfer Agents). Dovecot is only so you can view your mail in email clients on your computer instead of server, which is not really *receiving*. You can have a perfectly functional email system with no IMAP/POP server at all, you'd just have to read your email over SSH or whatever