SInce a lot of people are struggling with the puzzles, I will write here the solutions. Please do not read them if you didn't already completed the game. It would just ruin your experience.
First mechanism: click in this order, star-sun-moon-planet. Red the rock higher on the level to understand why
Second mechanism: today is 16/02. At day one, it was 15/02. Now it's day 2 (look the notes)
Third: you need to activate the lever in the first room, and only that. You will find a note of peter saying why.
Last one, the bomb: cut red and blue. You should try to understand what James Yellow means with the sign method. Maybe you sould what at the surname of the guys Lukas Red, Jones Yellow Henry Blue, Peter Green.
That's it. Hope you like the end of the game, it's the best part in my opinion