My question is about what levels of information you should reveal or be willing to reveal to your opponent for the benefit of the game you are in. To clarify this question I propose a scenario: I am playing TPS, and am preparing to "go off" on the second turn playing out a bunch of spells that would significantly influence my Storm count but would not necessarily let my opponent know I am playing a Storm based deck. At which point should a player start tallying Storm to reduce confusion and/or possible cheating in the end game procedure or doing something similar to this in a match?
Unlike many VA Q&A questions, which I believe have multiple correct answers that heavily dependent on context, I think this question has one clear right answer: You should start recording information in a way that's visible your opponent only when the amount of relevant information exceeds what you can keep track of in your head.
To use your storm count example, if you're storming up at 3, you probably don't need to be making hash marks on your life total paper yet. Once things start getting complicated with mana totals, spells interacting on the stack, and a storm count that's increasing all the while, jotting things down on a piece of paper probably makes sense. You're trying to compromise between two competing goals: (1) The overriding goal of avoiding confusion/forgetting information relevant to the game state; and (2) avoiding having to divulge information to your opponent.
(1) is paramount. You have to avoid situations in which disputes could emerge concerning the game state. It's your responsibility as a player to keep this information straight, and failure to do so can only bring negative outcomes, such as your opponent's interpretation overriding yours, or getting penalty. However, (2) is also relevant, especially if your opponent can interact to disrupt a Storm kill. You don't want to telegraph that this where you're headed. So, as long as you can keep everything completely clear in your memory, don't write down Storm count. But once any uncertainty about your capacity to do that emerges, it's time to start to minimize risk of confusion.
Similarly, if you know you can remember your opponent's hand after a Duress without writing it down, it might be worthwhile to try that. If you're playing someone you don't know, they might wrongly assume you're a scrub and start to take risks against you that they wouldn't against a name player, or someone who looked competitive. Also, they might think you don't remember the contents of their hand, when in fact you do.
Lastly, a point of advice to storm players everywhere: If you killed someone through storm, use a new piece of paper for your next match. It's one of the biggest tells I know of for combo to see someone setting up for our match and flipping over a piece of paper with hash marks and "B" counts all over it, with an opponent's life total that went from 18 to 0 all at once.