At my JFK GE interview, I was asked reasonable questions (e.g. name; where I work in the UK; where I live, etc). It mostly seemed like it was confirming everything on my application form. It felt quite formal but then again it should. It didn't feel as formal as the usual admission interview at the border though.
Assuming your flight is on time in JFK, then should be more than fine to get to your interview
I got across in 45 minutes from the AA terminal to T4, even when having to go through immigration.
There is a paper-and-pen sign-in sheet on a clipboard when you get to the GE enrolment centre in T4. You just write in your details and then sit down. There was no human interaction during sign in sheet- it was just placed outside the waiting area and you're directed by a sign to the waiting area. A quick nod to the other applicants waiting in there, and I sat down. I was on time.
About five minutes later, I was called in by name by a gent who had picked up the clipboard sign-in sheet- presumably he had just looked at the sheet and selected me as the next person who was on time. I noticed that some people had filled in the sign-in sheet that were late (the sign-in sheet asks for your time of arrival and the time of your interview). It wasn't too busy when I was there (maybe 4 people waiting, 3 people in interviews at the time). If you had similar situation then I imagine they'd fit you in but probably after getting through all the people who are on time. It must happen all the time and it wasn't particularly busy.
I would imagine you can talk to somebody at the enrolment centre if you really were late, but if you were 5/10 minutes late then I'd just fill in your details and sit down