Jame, a "watch" is not necessarily the same as a day-to-day job, though. For the IT guys (on the command ship), most were "on duty" during the normal hours. Because everybody was available, there was seldom an official "watchbill". However, at night and with liberty calls, they had to have a watch stood to ensure the computer systems continued to run. And, sometimes, they even took a turn as "watch" at some other duty - maybe a general duty that rotated among departments, or they were earning their warfare pin and had to be on the bridge, or the engine room, etc.
Rossthree - same as the others here - being crew does not allow access to the entire ship. Unless, of course, the size of the crew demands it. Heck, there're even passageways you can't traverse unless on specific business. Not to mention areas with classified information - and, NO, most sailors have no access to classified at all.
As far as awards for covert ops.... We don't have that many awards (in the US military) and those awards are given for so many different things that the only opsec issue might be a medal for valor during peacetime. So, they would most likely be given a non-valor-related medal, with a note in their classified dossier of the actual award.