Can confirm it's free. I tried it based on the GP comment. There are various ways to prove it is your domain: token sent to one of a small number of email addresses like {admin,security,webmaster}@, DNS TXT record, place a small file in the root of the website, etc.

The only extra bits I saw for the other emails on my domain was a plus address I'd used for last.fm which had been leaked. None of the other emails (wife, kid, family, etc) appear in any breach.

I'm slowly moving away from using my own personal domain as it's becoming an ever increasing burden. I'm also concerned that my wife/kid will be left with something they may not have access to, or would stop working at some point, if I suddenly dropped dead.

I had a domain registered and I got notices for about five email addresses - but after a while I was told I'd had too many localparts appear in breaches and I had to pay to upgrade.

It might have changed again now, but that was the point I deleted my account. The pricing list seems to imply a limit on the local-parts for a domain, though ..