"Is the client primarily looking for quantitative or qualitative insights?" - not sure how this question is relevant if at all. Most of the insights are coming from numbers
"Are we mainly concerned about finding the causes and then propose some solutions or should we directly come up with solutions?" - Irrelevant as well. There are no cases where you come directly with the solutions. Even in the case of the sales growth you first need to do the diagnostics. Consultants don't come up with ready-made recommendations.
I suggest asking the following questions:
1) Clarify the business model / how the business actually makes money. Even if you think you understand it, try to repeat it to make sure that you understand it correctly. e.g. if the case is about oil&gas company which revenues are declining, ask if it is Up / mid / down-stream problem. In this case, defining a revenue stream is critical to setting up the right structure.
2) Clarify the objective. Here make sure that your goal is:
- Has a time-framed
- Has / has no limitations
e.g. Should I invest 100k in this business for 1 year if I want to get 15% return?
3) Ask the questions that will help you build a relevant structure and remove ambiguity