I have replied below to your questions. As mentioned by Vlad, you should definitely do some live practice before the interview, that can help you a lot in improving, in particular for what concerns your communication.
The interviewer reads the case and I take a minute to structure my thoughts and tell hime how I will approach and structure the problem?
The process I would recommend is the following:
- The interviewer reads the prompt
- You repeat the information
- You clarify the goal, business model and potential constraints we have
- You ask for one minute of time to structure
- You can then present your structure
Can I take notes on my points and explain my thinking after that or should that be simultaniously?
Assuming you refer to questions asked by the interviewer, both at the beginning and during the case, you can always ask for 1 minute (beginning of the case) or 30 seconds (during the case) to structure your approach and develop it on paper. After that, you can present your points.
Can I do my calculations in detailed writing and should I explain every move (e.g. when calculating 910*840 - 128*240)?
You should present the formula without numbers, align with the interviewer on the formula and once confirmed it’s ok, proceed with the math. You don’t need to go though all the numbers of the math so far that you aligned on the formula before, just present the main intermediary results to align during the process.
What do do (seriously) when I am stuck, how to ask for advice in that case?
If you get stuck you should:
- Repeat all the relevant information you received until the moment
- Ask for one minute of time to think
- If still stuck, ask for help
Do I bring my own pen and pat?
I would suggest bringing them as backup, but you can normally use the ones the consultant will offer you.