Don't worry, you can easily dodge the teachers. If you wait a bit, you will see a balloon with ZZZ's appear above their heads. When that happens, they've fallen asleep and then you can move in before they wake up.
Hello! Mmm the tasks correspond to a week again, although there are some days where you can't do any task. But it should be less than two weeks of in-game time.
In the current version of the game, confession is not possible. But, in the future, I'll probably bring up both possibilities: the player can confess their feelings to Katsune or, if they don't, she will and then you can accept or reject her.