Love the game idea and it's all super neat. I think definitely making it more clear that there are things around you in the house that you can use to win the mini games (I sat there for a while confused on how to win, only to find out that you can't win during class).
I think you should definitely keep expanding on this game, even adding a computer where you can pick what type of game to play would be fun.
I think it would be beneficial to force the players into a tutorial at the start so they understand what is going on/what they have to do. I feel like you could really delve into the narrative with a tutorial and mess with the player.