I done well in my Higher maths (A band 1) but didn't try so hard in Advanced Higher (B). Not sure if it's at the same level as A-levels but nevertheless...
1) People do well if they work at a slow pace throughout the year, doing past papers in each topic throughout and feeling confident, being oraganised with their work, doing homework on time and keeping on top of things. When it comes to exams, they have less to worry, and is just a matter of refreshing their memory.
2) Just remain calm. Don't think about the exam too much, get a good sleep, have breakfast and finally refresh the rusted memory on topics you think might come up in the exam before you take the exam.
3) Hmm I wouldn't see any harm. Probably best having water in the exam though.
4) Maths was the one I done best in, on terms of final grades. I put in more effort but it felt less, so my advice is get stuck into your work, listen to the teacher and ask questions if there's ANYTHING you don't understand. When you have a full understanding for a topic you could easily do the past papers and then you'll be able to exceed the average past papers and go onto more difficult and challenging questions. I was quite a perfectionist and made sure I knew everything I was supposed to know/learn.
If you can do the challenging past papers, you'll think the exam paper is easier than you expect it.