We can see IP addresses, but not private PMs or your email address. It should be noted, however, that none of this kind of ‘private’ information is readily or immediately available to us. When we click on a profile, it looks almost identical to the ‘Profile’ pages you guys see.
The main difference is a small button that enables us to dig deeper on a particular user, if necessary; a suspected returning troll, a participant in a spam setup, etc. Clicking on the button takes us to a moderator page that lists all of a person’s posts (censored or not), their location, the color of their underwear, that kind of thing.