yes.
When starting the game will ask if you "know the secrets to this world", click "yes" if you have played all the story including the true ending (this will unlock spoilers).
From there, on one of the earlier days, you will go to get your notebook from class at night, iirc this is the first main choice to chain new routes (i think this triggers Saya's though it would be for all, use a guide if you must, its been some time for me now).

Just remember to click yes on knowing the secret when you first begin the game, its very early in the opening and will need you to erase your entire file (in the directory and cloud) to undo this.

It did not ask, though admittedly, I'm only a couple of days in. I did manage to get riki to retrieve the notebook on the first couple of days though.

Pretty sure this doesn't happen. At least not anymore. It didn't for me at least.