When asked a fit question, how much time is it ok to wait & think? Or is it expected to reply immediately without a pause?
in general you are not supposed to ask for time before fit questions - the expectation of the interviewer is that you should have prepared them in advance. Having said that, if you receive a question you have no idea how to answer it is better to take 10-15 seconds than to answer in an unstructured or incomplete way.
If the question is a simple walk me through your CV, or why BCG etc. then you should reply right away. However, if it's a more complicated question such as tell me about a time when you showed your leadership skills, then you can always ask for a moment to gather your thoughts (e.g., 30 seconds).
Adding to the other answers, if you do absolutely need time, you can "buy" it. Say, "Oh, that's really interesting. I kind of think in that answer in two ways. There were two periods in my life where that happened, and I'm just trying to think which one applies best. There was x and y, but I actually think y is best because...."
Find a way to talk a little, aim to even drop in some skills or experiences, then jump into answering. As the others have said, this obviously doesn't apply to a "Why company/consulting" or resume walkthrough question.
- If it is the part of the mandatory fit questions (e.g. personal impact at McKinsey) you are not supposed to take time
- If it is a non-conventional questions - it's fine to take time, but better answer asap
Besides being great at case cracking you also need to convince the interviewer that your personality fits into a case team or in the company as a whole
Getting Up to Speed
In order to repeatedly demonstrate prerequisite skills under the pressure of a real case interview, you need to learn the basics and practice cases.