Room inspections don't really happen as often as most people think, and almost never in a war zone. Not in the Navy, anyway. If you get a room inspection and you're out of AIT (we call it A-school in the navy), it's because someone tipped your command off that there's something illegal going on in there. They'll call it a 'health and welfare' inspection. And no, they absolutely can't check your browsing history during a random inspection. I wouldn't let them touch my computer, and I'd be well within my rights. That's personal property and they can't mess with it without your permission. Not that they would, though. Most inspections focus on "gear adrift" (shit that's not stowed properly), stinking-ass laundry that hasn't been done in months, and drugs/drug paraphernalia.