One thing I found helpful was to....relax. For example, I spent months revising for my psychology and was really stressed for it and I never really answered the questions as per say but instead just regurgitated my pre-made essay plans. Whereas for my English exams, I did stress for it but that was during revision time. I left like 2 days before the exam with light reading of the subject to clear my head and that REALLY helped. Just make sure you go into the exam with a clear head (not clear as in everything erased) and take a deep breath.
For the essays, it IS a prerequisite that you plan. If you fail to plan then you plan to fail. How you plan is really up to you, be it a mind map, bullet points or whatever.
For introductions I think it's good to provide a very brief overview of the text according to the essay question. Be concise and to the point in your main paragraphs, don't regurgitate the text but instead elaborate it, extend it, look deeper into it, what's the underlying meaning of it. Refering to the person who mentioned the teacher telling you not to start new points in your essays, I think that's quite silly to be honest. Of course your allowed to start new points BUT only at the start of a new paragraph. If your making a new point start a new paragraph. For the conclusion, you just sum up all the points you made briefly and tie it all together and say whether it was successful or not.