the-witness
Immediately after you leave the entry are there is a huge door with puzzle on it. You learn how to solve it buy following the path past it to the next puzzles. If you return and to it successfully it opens the door to a room with table like chest where you get a piece of paper with a zig-zagy solution to a bee-hive like challenge to (i'm assuming) a future door.
Why is this there, where should it be used, and what difference would using it makes ?
There is not really a point of no return you need to worry about. While there is a point that triggers the ending which you then can't abort, you'll be able to recover the savegame and complete the other puzzles (and I believe this is how the game is intended to be played).
When you do complete the game it will quit (on PC at least) and when you restart it, you'll start from a fresh savegame, but you can then enter the menu and load your previous savegame. That last (auto-)save will always be just before the actual point of no return. The OP said the game loaded that savegame automatically upon restarting the game, so maybe this was changed in a recent update. (Also, I vaguely remember from some YouTube video that the PS4 version will just present you with the loading menu right away instead of quitting the game.)
If you really want to know the "point of no return" that requires you to load the last save:
There's an elevator in the water, that is activated via two simple "puzzles" (they're just straight lines, I think). When you activate the elevator, then the ending sequence starts.
Some spoilers here, you might not want to read them until you've solved a lot more puzzles:
The same thing is true for the alternative ending. The "point of no return" here is actually a few minutes of gameplay worth before the actual end of the game, but when you load the savegame you'll still start from before that point. The next spoiler block contains that point.
When you solve the "hidden (environmental) puzzle" that involves the sun and the structure around the gate of light in the starting area, you open up the final area that leads to the alternative ending. This can't be undone, and you cannot leave the starting area once you do, unless you load that savegame.
I think the most spoiler-free reformulation naturally would be spectrograms of the sound records. Since, they allow you to hear with your eyes.
I made them and checked that you can see (on spectrograms) all the patterns, which I was able (hardly) to hear (in the sounds), that means the puzzles must be solvable with my spectrograms even if you hear nothing.
Note:
1. Many puzzles becaume trivial for me once I saw the spectrograms, but some still are hard (see note#2 below). I think this is perfectly normal, since exactly the same was true in the other parts of iland: most of the puzzles where just to make sure that you understood rules correctly, not to be a challenge. Also I think this was the case for a musician, who would hear sounds.
2. Even once you figure out all the rules correctly you still may need some trial and error to make sure if you see correctly, but these are minor (much much smaller than I had to try using my ears).
3. On the spectrograms below you will see time on horisontal axis, frequency on the vertical and the color shows intensity of the sound component.
1.1. S1P1 (set 1, puzzle 1)
1.2. S1P2
1.3. S1P3
1.4. S2P1
1.5. S2P2
1.6. S2P3
1.7. S2P4
1.8. S3P1
1.9. S3P2
1.10. S3P3
1.11. S3P4
1.12. S3P5
1.13. S3P6 (here I decided that 2 sets is not enough and made 4)
Best Answer
The piece of paper gives you a solution that you can enter into the hexagon puzzle below the Windmill.
This is completely optional.