How do people remember the symbols beside the cannon without slowing down?

We just draw them on the paper.

Do you just draw a really rough sketch of them?

Yup, just few "random" lines to distinguish them later.

I have created my own "cheat sheet", where I have drawn all the available symbols for the cannon puzzle, and then I write numbers next to them depending on which order they appear in!

What about the memory/bear puzzle?

You don't even need to complete memory cards puzzle. You just need to write down how many of each symbol there are.

I'm aware of that, but what does your notes of the number of required symbols generally look like? (I should've been more specific with my last question)

'cauz when I counted the amount of symbols in my casual playthrough, I used tally marks, what about you?

I imagine you do the same.

I just draw all of the symbols on my notes before the run. And just put dots/lines next to them (prison kinda style lines) to count them and note them asap.

Funny thing I remembered. For the radio puzzle, I never used notes to remember the solution. I know you don't need to go to the radio on the side of the lake, but it is important for backtracking.

For the radio, it's much faster to just scroll through all radio stations, one by one, to find the correct one, rather than driving all the way up in the radio car to hear which one it is.