Answer

Wow, what a barrage of questions. I’ll answer only on the level of principle. First, this is not a place for general instructions. Refusal, by definition, is a personal act about which a soldier is supposed to make a decision based on his own judgment. Therefore, my opinion about the disengagement and about all the considerations you raised is not important in this context, because what determines the matter is the view of the soldier who is considering refusal. So the discussion is about a soldier who, in his opinion, sees the disengagement as problematic for the reasons above and is undecided about what to do.
First, as a starting point, in my opinion it is clear in principle that there are situations in which a soldier must refuse an order. He is supposed to weigh his considerations, take into account that maybe he does not know everything, and of course also examine the consequences of carrying out the order (how problematic it is in his view) and of refusing it (undermining the structure of the army). But if those conditions are met, he must refuse. This is an obligation—moral, of course, not legal—and not merely a right. A view that does not recognize the right (and in my opinion, the duty) to refuse—what you described as “a soldier has to obey orders”—if taken to the extreme, is pathetic and dangerous fascism.
I already wrote here in the past that I would not want to go to war with soldiers whom I know would never refuse my orders. That is a recipe for a robotic army that can reach morally atrocious acts and foolish acts, and in fact it is a recipe for orders of poor military and moral quality (because a commander who knows he will never be refused will not hesitate to give any order that comes into his mind).
The consideration that most of the public rejects the order and that the government is acting without authority has some substance in principle in two situations: 1. When the other conditions are not present (I agree with the order but most of the public opposes it); otherwise one refuses because of the other considerations. 2. When the other considerations exist but are not sufficient to justify refusal, and one wants to add this consideration to them.
But this consideration is very dangerous, and I would be very hesitant to use it except perhaps in very extreme cases (as opposed to conscientious refusal based on another consideration from among those you raised, which can be used more readily—though of course that too must be used sparingly). First, you do not know whether the majority of the public really opposes it (everyone is sure the public is with him; our sampling is biased according to our own views, our friends, and our surroundings. Beyond that, public opinion sometimes sways with the wind). Second, even if most of the public opposes it, there is still reason to say that the government may act differently because of “things you see from there” (as Ariel Sharon used to say).
Notice that in practice, usually the one considering refusal is the same person who opposes the order, but according to this consideration, even someone who supports the disengagement should have had to refuse, because most of the public opposes it and therefore it is illegal. And of course the reverse is true for someone who opposes the order but estimates that most of the public supports it. That of course does not happen, and that means we are very biased in these considerations.
To conclude, I will note that there is a difference between the considerations: if you refuse on grounds of conscience, as distinct from an order that is manifestly illegal, you must accept the consequences, because in that case the order is legal, but it conflicts with your conscience. The legitimacy to refuse in such a case is outside the legal framework, and this is not the place to elaborate. But refusal based on the last consideration already concerns a manifestly illegal order, because according to your legal theory this is an order that may not be obeyed, not merely one that your conscience forbids you from obeying. It is not binding at all, and issuing it is itself a violation of the law. That is another reason why such a consideration is much more dangerous than the others. Here you are essentially making a claim about the legal system as a whole and saying that everyone must refuse regardless of their outlook, and not merely taking a personal step and accepting the consequences as in ordinary conscientious refusal.