HSK Note Taking and Section Skipping
Here is where the rules of the HSK get wishy-washy.
Technically, no, you cannot take notes. And no, you cannot skip sections (e.g., you cannot spend extra time on the reading section going back to the listening section).
However, these rules are not usually enforced, nor are they really set in stone. Although the reading and writing section are on the same text paper, you are not supposed to be free in dividing your time among them; you have a set amount of time for each section.
But, this does not stop students from moving back and forth or taking notes (e.g., at the five minute break after the listening test, some students may go ahead and look at the reading section).
If your goal is to get pass the HSK, you honestly should be prepared before you come. You shouldn’t need to skip around or take notes.
That being said, if you feel you need to skip around or take notes, no one is going to stop you.
However, if you are asking this question, I would say your heart is in the wrong place. Your focus should be improving your HSK ability, not on bending the rules to improve your score.