Bug fixed! It was another mistake of mine, for a change... I hope that this time there are no more serious bugs.
Once you meet Nana, you have to go talk to Katsune and select the "Special" option, which is used to tell her about special missions and rivals when they are available. I guess I should explain it in-game.
How do you get Katsune to follow you to the cafeteria, classes, etc? The game should not allow it.
I'm glad the routes are working properly at last.
Thank you for all your help reporting bugs. I hope you keep playing when you feels like it!