The USCIS officer(s) is (are) at a table just inside the side door of the courtroom. As people arrive before the scheduled time of the ceremony, you will line up outside the side door and a couple of people are let in at a time to meet the officer(s). He / she will go over your responses on the oath notice form and ask for your green card and then you can sit down in the courtroom to wait for the ceremony part (your guests enter at the back entrance and you can sit together once your processing is complete). I don't recall seeing anything in the way of immigration files there -- only the naturalization certificates and other materials they hand out at the ceremony. They did have a report that listed everyone on it who was scheduled for a ceremony, and possibly that report has on the # of days outside the U.S for each individual up until the time of the time of the interview.
If I were you, I would bring the copy of the N-400 that has your exit / entry dates on it, and any other summary you have of the dates since you sent in the N-400. Bring your passport(s) too -- assuming most of your trips have stamps to help document your absences. In all likelihood you won't be asked for this, but as you know, it's best to be prepared.
Do they give your naturalization certificate then and there?