Drafting without being able to look at your picks?
Competitive rules does not allow players to look at their previous picks during or between picks, only between rounds (between each boosters).
You are also not allowed to reorganize your picks until the end of the draft.
These rules prevents cheating and/or player mistakes while drafting.

In a non-professional environment, these rules are optional, so be sure to check with your LGS which one are enforced.

As for what to focus on remembering, the best answer would be "everything".

Curve, removals, the pace of the game, and color synergies are all very dependent on the current format.
You can find format-specific breakdown and strategies guides on the internets, but the best way to improve in real life drafting is experience.

From my experience, if you were to choose one thing to track, it would be your creature/non creature spells ratio, as it is a very important part of deck building in limited, regardless of the current format.