For everything you've said here:
1. Those aren't here yet, but they're on the way, don't worry!
2. It might be a bit too late to implement something like that at this stage, but I'll see what I can do.
3. The reason for all that is because of location. Since with the acceptance of Bailey who has narrative purpose, everyone other classmate or the Principal have you moving around a lot. So it's easier to remember an event then to try and explain why we find ourselves in the exact same situation all over again. Where as people like the nun rarely leave their spot, which is the major difference in the characters.
4. I'll definitely consider adding a button both to let you return home immediately as well as an option to skip right to the next day. Look forward to hopefully seeing it next update!
As for the rest, I look forward to showing you how the green haired girl changes the story. And as for the Saki event, it should be there. I'll look into it.
And finally, for the thing with the story mode, that's weird and I'll try and fix it right away. Thank you for letting me know your thoughts and I hope you continue to enjoy Doing Things My Way!