A game like this would work better if players didn’t have the solution to each puzzle right next; sprinkle the info earlier, before the player even sees the puzzle.
Letting players choose from two or three different tasks they can do at the same time helps break the linear feeling; it gives players some semblance of choice. They should be able to pick which one to start with, but they need to finish all of them to move on.
Also, for any text dialogue on the screen, if you don't wait for player input, make sure to keep it up longer than you need it yourself. Since you know what it says, it’s easy for you to skim through, but players are seeing it for the first time and might miss important details if it's up for only a short time.
Good concept for the theme.