First off, I wrote in the games description that this is my first game. This is the reason behind why there is no content behind the successful completion of the puzzles. I used this game as a project to learn the mechanics of the engine and implemented them as I went. HOWEVER, in the next character, I've changed this so that there is content for successful actions and a "Good ending" is being implemented. I'm planning on doing a devlog soon, but the next character will function a bit differently, and overall, will contain more scenes and scene variations.
Secondly, Nagatoro is someone I've considered, and will likely be added in the future, same with group settings.
Lastly, you're absolutely right, the third section of the puzzle is blocked. I'll fix that now. Thanks for letting me know!