Just to expand on this thread a bit:
After getting the cool kid's bandana, run around for a while and get back to the classroom, there will be a special cutscene after interacting with the teacher. You can repeat and come back again for Leah to teach as a substitute teacher.
After Sanura learns the special skill in the basement of the mansion, the player can now go the milk farm and remove the bolder which is located at the back of the farm. There is a special dungeon at the back. Clearing the dungeon also allows the player to harvest a very rare fruit, which could be used at the Witch's Academy during night time (hint: Witch's Academy night time basement, use Leah).
Just a question by the way, anyone figured out how to communicate with the cats at the Witch's Academy? Can't seem to play as Sanura there. Also, the spelunking twins who are located at the entrance of the pyramid asks me to collect a "Neko Idol". I just couldn't seem to find it for some reason?