Hey nhih, thanks for playing my game and leaving a detailed review! I think this is my first puzzle game, so it's nice to know that the levels were engaging to solve and the game feel was great.
The music was supposed to be a bit ambient to create a calm feeling, I didn't look into more options but found this one pretty charming.
Since the jam ended (and I actually won! yay), I updated the game with a few more feature to adress your two points. So now the game has a level select screen and that particular UI element is now clickable!
Thanks for the ideas and hope you can check the new level!