I always think, though not in the context of war crimes, how two friends of mine related in Basic Training that the drill instructors would give them strict orders to not let anyone through on guard duty who didn't meet some criteria or another, and then other instructors would come by and attempt to badger and bamboozle the poor trainee soldier into letting them through (and God help any who was stupid enough to let them through).
Rules can be inflexible, but they're also a barrier against arbitrary abuses. Our abuses have to be regular and systemic, dammit!
Not in the US military, and I'm sure others as well. What civilized nations are you referring to? I can only speak to the US, but enlisted soldiers here take a pledge to follow orders, while the officers are actually the ones to take a pledge to uphold the US constitution.
No, they absolutely do pledge and affirm that. Not sure what that person is talking about. It's definitely, at least on paper, expected for individuals in the military to refuse to follow unlawful orders. What happens in practice is another story. See: entire history of US military action.
You are not required to obey an unlawful order and in most militaries you are required not to. If you get court martialed it shouldn't be a problem since you were in the right and not the officer issuing the unlawful order.