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So I am studying the "Introduction to Logic" section. So when I'm at the exam, after I've gone through the steps to eventually know the relationship in the "sufficient condition➡️necessary condition" form, should I note this relationship with an arrow down on paper physically for further use or should I just remember it in mind?
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I think you can use question types to your advantage. When I see it is a SA or a PF question (there's a few more) with lots of conditional logic in the stimulus, I can definitely expect my understanding of lawgic to become relevant. That's when I like to write it down. On the other hand, there are questions with conditional statements that aren't even relevant to getting it correct. I think it's intended to waste time and I've definitely done that before. I also think memorizing conditional statements becomes easier with time and practice.
I'd say whatever works for you at the time. There will absolutely be times where you will want to diagram it. But as long as you can hold it in your head (don't forget the contrapositive!) you're good.
Also tip: Since you are new, train your self to hear ALARM BELLS when you see a conditional indicator. That will save you points.