Dear Future Consultant,
At the beginning, it is tough to draw the line between the so called "initial questions" and the "structure." To master this skills would require practice, and what you have to ask on each side of the line will depend solely on the information the interviewer gives you and your preparation.
I agree with Francesco's initial approach and Dane's comments, but I would like to build on both comments and propose the following approach to any case, which also applies to a profitability case:
1) Rephrase the business problem, if you receive any numeric goals, try to do some math beforehand (e.g. "the client has hired us to increase revenues by 15% or US$ 100 MM)
2) Ask for secondary objectives, but not just ask but be proactive and state which could be some potential secondaries targets for the case (e.g., "There is an underlying goal I should be aware such as "increasing market share since the company's strategy ..... ")
3) Ask clarifying questions: This requires practice to "draw the line". Usually, I recommend not to ask more than 3 questions that are relevant or critical to understanding the business case. Nature will depend on the case, your preparation and, even, the interviewer personality. Some examples are: in which country the client operates? Which is the size and profitability of the customer? Can you explain to me more about the disease that this product is aiming to cure? How long will be the contract between the government and our client? ... etc.)
4) Lay down your structure: In a profitability, case do not stick only to revenues and cost, otherwise, you will never stand out from other candidates.
I hope this helps in your preparation,