I need help with two problems
How to assert yourself to your boss/supervisor without appearing impolite.
How to decrease stress level before a meeting where one needs to raise some difficult questions in front of the boss.
It is always a fine line between assertion and aggression, and it’s even worse when your manager is involved.
I’m not sure what the context is to your question, why you feel you need to assert yourself. I’ll assume you don’t feel you are being treated seriously by them, or they are not taking account of your opinions.
There are a number of general ways you can get yourself taken more seriously.
Conduct yourself with authority. Dress well, behave well. Act as if you have authority and deserve to be given credence
When you want to make a point, or win an argument, be very clear about your position, and back it up with facts and evidence to support your case
Don’t allow yourself to be rushed, take your time to formulate answers and arguments
Pay attention to your body language. Look relaxed and calm. Make sure your voice does not rise when you are challenged or stressed.
Treat your supervisor with respect and perhaps they will reciprocate.
Inclusivity is a good tack to adopt. “How can we resolve the situation?”. This puts you on the same side as your manager, rather than in opposition to them. So you don’t need to assert yourself, you are working together to solve a problem.
Decrease stress level
There are a couple of well-known techniques here. One is being properly prepared for what is going to happen in the meeting. I’m assuming this a meeting between the two of you, so you have a fair chance of controlling the way the meeting goes by preparing your “difficult “questions carefully. Know what the likely responses are and how you will deal with them.
Think through the various scenarios that will occur, and know the parameters you are prepared to work with.
Be prepared to say” Can I think about that and get back to you? “
Another technique is breathing deeply in the few minutes before the meeting. This seems to have a calming effect on the body
Another trick is to visualise a favourite calming scene, such as a beach, meadow, mountainside