1. Let me first start with a general remark: whether an case is conducted in the interviewer-led or interviewee-led manner is irrelevant to the structuring and for how to deal with hypotheses.
Moreover, stating a hypothesis for the overall problem only makes sense if you really have something to ground your hypothesis on! This is very rarely the case, since case prompts tend to be quite vague at the beginning. Just stating a hypothesis for the sake of it serves no purpose! It would just be a shot from the hip - and this is something you should avoid at all cost during an MBB interview!
If the question is about finding the reasons for an observed phenomenen (e.g., fallen profits), then you can rather say “I would like to first identify the numerical driver of the problem, which can sit either on the revenue or on the cost side (or both). Based on this initial assessment, I would build a hypothesis on the underlying reasons for the detrimental development, then verify the hypothesis, and subsequently derive measures to address these reasons in order to reverse the trend.”
If the question is eseentially a go- or no-go-decision (e.g., "Should we enter the Brazilian market?"), then a MUCH better approach than a blank "Yes/No"-Hypothesis (which feels stupid anyway, right?) is to define the criterion according to which the question can be answered. This implicitly comprises hypothesis-thinking, but in a much cleaner way. All you have to do is to
(1) narrow down the question,
(2) define the criterion according to which the question can be answered with "yes",
(3) outline how you can test whether the criterion is met.
That's it! This is how you address strategic questions without shooting out non-substantiated hypotheses (or rather wild guesses!), while still being super top-down and super efficient.
Hypotheses then are used all along the way of performing the actual analyses! But it is not hypotheses on the overall question, but hypotheses on the various sub-aspects which you need to test in order to eventually answer the overall question.
2. This depends on what you are actually asked. If the interviewer asks for your "approach", then it is all about the logic, and not about brainstorming endless lists of bullet points. If you are asked to list out "which elements to consider?", then this is more a brainstorming then a real case structuring. I would always recommend to verify this with the interviewer - no problem with asking. :)
3. It is not about the number of ideas, but about to show your ability to come up with a sound logic into which a rich set of ideas can be conceptually fitted. Whether you then put 2-3 example ideas into each category or more is not important.