Thank you so much for your detailed feedback! Just reading this once is enough to brighten up our day.
All of the puzzles have their own unique solutions. That means they have only one correct solution for each of them. So it's possible to solve them, it's just that the third one's difficulty is quite high compared to the other two.
Also, the UI is temporary and is expected to be improved a lot in the future. Please looking forward to the new look.
Again, thank you so much for all these kind words, Adam Kehl!