Very good question! But dont look to “react”. Rather learn to “respond”.  There is a big difference between the two which most people dont get. Most people are reacting and not responding. Response is conscious, well thought through and you are in control.

So, regardless of what challenge the interviewer throws, receive it, spend some seconds to look at it, analyse it and then respond with appropriate answers or reject the challenge politely. Its totally fine to take some time to digest the challenge. If you are in reaction mode, you will try to answer or start talking straight away. 

You can buy some additional seconds by asking a clarifying question/Yes or No question or requesting the interviewer to be specific (if they are a bit vague). Dont overdo this. 

This will come with practice.

In addition have a look at this article for some broad advice on managing interview nerves/anxiety- https://www.preplounge.com/en/articles/job-interview-stress

(editiert)

Remember the objective/question - If they ask a question, listen intently and lead with an answer. When working through the case, remember everything you do should be focused on the objective

Structure your thinking - When thinking + speaking, use structure to organize everything. By grouping things and talking in buckets you'll get your point across more concisely

Signpost - If needing to communicate multiple things, first state those x things! Then, afterwards, dive into each. So "I"m thinking about this in 3 ways. Way A, Way B, and Way C. In terms of Way A...."

Remember less is more - Think about longer sentences/phrases you use. Reflect on how to make them shorter. Much like you edit an essay, edit your speaking. Why use 5 words when a well-placed single word encompases that? Build your vocabulary (especially business vocabularly) to be able to use key words instead of wasting time "explaining" a concept

Practice with others - Tell others that you're working on this. Ask them to force you to be concise. So, tell them to interupt you if you're rambling! Record yourself for answers and listen to yourself....look for ways you could have been quicker.

Take a few seconds - gather your thoughts. Perhaps right them down. Take a quick breather to better formulate and then articulate your thoughts

1. Pause before speaking to gather your thoughts - the time may feel like forever for you, but it's not nearly as long as you think. Leverage filler sentences such as "that's and interesting point" to buy some time if needed.
2. Frame your answer - Generally, MBBers say "There are 3 parts to this". Then, they highlight in 1 sentence each of the 2-4 points
3. Iterate through each point - After framing how you're going to answer the question, then answer it by diving into each "part" in the order you summarized each.

(editiert)

Ultimately, you need to stay ahead, show ownership and drive the case. This includes preemptively addressing these points before they’re being raised by the interviewer.

Of course, it’s not really possible to avoid all questions because it’s part of the interviewer’s routine, irrespective of candidate performance. Especially the “what else” question in creative brainstorming scenarios (you could have 100 original ideas and they would still ask).

Bottom line, learn from these question and make them your own. And when you do get “pressure tested”, make sure you’re not getting flustered and fall behind losing all your drive. 

With time and practice, you will learn how to stay poised! Best of luck!

I think Lucie and Adi's answer's are quite strong - just wanted to reinforce that those are not “pressure tests”, and are an integral part of the case interview. They are actually questions you should be asking yourself. And great candidates answer them without being prompted. 

To give you an example: “Is this a reasonable number”. Most candidates think we're testing calculation ability in market sizing problems, for example. Well, that's the least important skill we are testing there, as we have excel for that. What we really need is an analyst that can look at excel's output and have good judgement and be able to evaluate whether the number provided makes sense or not.

“What information do we need” will usually come after you were a bit generic on your suggestion on how to move forward within the case.

Hope this helps!