To anyone asking- YES, it is possible to get all gold without cheats! I just did it, so I can confirm it's possible.
Here's a helper guide, written to the best of my ability.
Simon Says: (flashing yellow stones)
This game is just memorisation, nothing fancy. I imagine you know how to beat it, but if not, just watch the pattern it gives you and repeat.
Hints for perfection:
I'm pretty sure the final rounds are humanly impossible on the default speed. Turning up the speed gives you more time to input, at the cost of less time to view the answer. Again, you'll need this to get the final golds.
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Circles: (the one with lit stones in a circle, surprise)
This is a puzzle, where you want to get all stone in the circle lit. Whenever you click somewhere, it switches the state of 3 stones- the one you clicked on, and the two surrounding. You need to use your flipping power to light them all up.
Hints for perfection:
This one is hard, but VERY learnable. Unfortuantely, there's not a lot a guide can do to help. You just gotta get a feel for what positions let you solve, and then figure out how to reach those positions consistently.
...If you wanna learn a cheese strat though, the most reliable pattern I found for solving is two yellows next to each other, and everything else grey. How do you get the circle in that position, though? This will be... difficult to describe with text alone, so please bare with me.
For the sake of learning, start with one space grey, and the rest yellow. (if you need, keep resetting the puzzle with the restart at the bottom until this configuration happens) Once you've got that, click in the single grey spot- and watch it split into two! From there, choose one grey to keep clicking (and ignore the other one). Each time you click it,, it'll appear to move one space to the side, with a yellow light trailing behind it. Keep doing this, until you only have one yellow remaining.
From here, click one more time on either side of the yellow. This will turn your single yellow into two. This is perfect, since this gives us 6 grey spaces- and we can easily solve the puzzle in two turns!
Note that you do not need the almost-all-yellow starting position for this to work. It can work in many other configurations, so if you're ever stumped on a puzzle, try it out and see if it works. Likely, it will, and will be faster than fumbling around.
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Stone Radar: (stones next to each other, no simon-says hint)
You gotta light up all the stones by clicking them in order. Each time you get it wrong, you restart the pattern again. Just try things and learn the pattern overtime.
Hints for perfection:
You can't plan this one. It's just luck. Sorry.
There IS some tech though, that can be moderately helpful. You notice how, whenever you click a wrong stone, it either flashes red or yellow? There's meaning to that!
If it flashes yellow, that means the correct stone is touching it. (giving you a small hint for your next attempt) If it flashes red, the correct stone is not touching it. (telling you to search far away)
And yeah that's pretty much it. Otherwise, brute-force it until you get lucky enough.
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Picross: (has a grid with numbers, and clickable spaces)
The most unique puzzle by far! This is essentially a math equation, where you need to get each row (the horizontal lines) adding up to its number on the right, and each column (the vertical lines) adding up to its number on the bottom. As shown at the top, the first space in any row is worth 1 for that row, the second is worth 2 for that row, etc. Same goes for columns, but their numbers are on the left.
Tips for perfection:
Again, unfortunately, you just gotta get good at thinking quick here. My biggest tips are:
If you're stumped, only focus on rows and try to get those working, ignoring the columns completely. Then, try to solve columns. Then, try to solve rows again. Eventually, you'll find a solution that solves both.
More situationally, some numbers have obvious solutions you can input right away, and know they're right. For instance, 2! The only way to get it is by putting a dot in the 2 space, and leaving everything else in that line blank.
The special numbers I found are:
2: Only fill in the 2, leave everything else blank
7: Definitely needs the 4 filled, but everything else can vary
8: Fill in 1, 3, and 4. Leave 2 blank.
9: Fill in 2, 3, and 4. Leave 1 blank.
If you can, fill those in first. It'll give you less room to fumble and make the overall solve faster.
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Hope that all helped someone out there :3