The lockers at my test center were right in front of the front desk, so there was always someone there. It's not like they were staring at me during my breaks to make sure I wasn't studying, but they definitely would have been able to see me do it if I had tried.
When it comes to bringing things into the test center, it's better to be safe than sorry. Technically you aren't even allowed to bring your own tissues into the room, so empty your pockets into your locker.
For food, I brought a banana, a nut mix that had some chocolate in it, Gatorade, and some water. Beware of drinking too much liquid though - it's a long test and any unscheduled bathroom breaks won't make the timer stop. You should take your time on your breaks so that you can relax a little bit before going back in. Having said that, though, make sure you keep an eye on the time if possible: I was four minutes late coming back from my first break and two minutes late coming back from my second break