The opening scene, was that an illusion projector to make the house and the surroundings look nice or an invisible biosphere bubble that allows vegetation to grow inside.
The main girl is very annoying and stubborn. As long as they all were short skirts, I don't mind.
How can a planet worried about war not see a spaceship take off from the planet? Why didn't they ask the one student that has pilot training to fly the spaceship?
If the girl can generate wormholes, why is she always late for class?