can we use sensitive for the first blank? I feel all the options for the first blank mean almost the same.., how do we differentiate among them?

That is a good question. The sentence is a bit tricky but not the end of the world to grasp the meaning.

I.E: the CEo needed to consult and take advice from the closest allays to make a the decision because the situation is important to cope with.

Now, a clever reflection for the first balonk is that A and B are synonyms, therefore, first thing fist we need to have a decision between A/B and C. If we know that A or B are wrong we can eliminate both. using the probability concept we do have 1/2. However, IF the answer is NOT C then we need to have a decision between A and B but that is after our first assessment. For now is suffice to say that

Back to the question why cannot be A or B alike ?

Well, delicate means something to handle with care and could fit here. However, we have The (i) _____ nature of the situation we have that the situation has some kind of peculiar to it. Therefore a situation is not delicate by nature. It becomes delicate but here the situation is intricated per see, on its own, or by nature. That's why C is correct and A/B are both wrong