As far as I know, you just have to enter your email address and check their databases if your email has been breached or not. And then they have this services that will let you notify when your email has been breached.
No. You don't get my idea. I meant if you don't enter your email address on that site, they likely don't have your email address in their database. Maybe they have it on database or maybe not before the time you enter and search. It is only assumption and the prevention is protect the privacy of your important email address.
As same as when you use your bitcoin address, when you lost its anonymity, you can not get it back.