They have to follow the commander's legal orders. Whether they agreed or not should be immaterial.
A strike isn't an order, so I'm not sure how that thought progresses things.
Commander tends to retain... command authority. The crew doesnt agree, they execute orders.
Hence the phrase 'burden of command'
In some situations, disagreement early in the decision making process could be beneficial to all participants. See https://en.wikipedia.org/wiki/Disagree_and_commit for context (a principle used at Intel and Amazon).
Yes - which is why there is a concept of good and bad leadership.
Commanders shouls consider all forms of feedback on a decision