You don't need any auth to send an email from your domain, or in fact from any domain. Just set whatever `From` you want.

I've received many emails from `root@localhost` over the years.

Admittedly, most residential ISPs block all SMTP traffic, and other email servers are likely to drop it or mark it as spam, but there's no strict requirement for auth.

It should not, but it's usual to configure random services to send mails to users, for instance for password resets, or for random notifications.

Another thing usually sending mails is cron, but that should only go to the admin(s).

Some services might also display the host name somewhere in their UI.