For the US military its not illegal to refuse to follow an illegal order. The US Marines have this drilled into them, not sure about the other services.
Sure, but you may have next to no information in that little amount of time to make the determination. For all you would know sitting at the terminal, that Russian/Chinese ICBMs were on their way. There was a Radiolab episode about this recently. It's tough to become one of the officers in this position and are heavily selected for those that would act unquestionably on orders. Any hint of questioning orders/superiors/the system gets you kicked out. This was done so that there would be no question in our rivals minds of our intent to follow through with the MAD doctrine.
It's one thing to pledge to this, yet another to actually be in the silo with the alarms blaring and the the orders coming in with seconds to spare. It's impossible to predict in advance how someone would respond to this situation.
