Nope.
Architectures like OpenID "phone home" and report your movement across the web.
Persona was explicitly designed to be privacy preserving.
> Second question, if an attacker knows my Yahoo password, can he potentially login to _all_ Persona-powered websites with my email then?
Yes, if an attacker has your yahoo email address and password, they can log in as you. BUT, you can take advantage of two factor auth from Yahoo as well as other security features they provide, to keep yourself safe.
However, if you use the "login with Yahoo" button (or Google or Facebook), then yes, they can track all of your activity.
To your second point: great question! No, the attacker cannot. We still protect your other email addresses with a Persona password.
But Yahoo still knows that I'm on that website.
Wait. So, my email provider (Yahoo) can now keep track of every website I login to, if he wants? How can I stop Yahoo being the middleman?
Second question, if an attacker knows my Yahoo password, can he potentially login to _all_ Persona-powered websites with my email then?