Tetsuro's running gag (his characters always die shortly after they appear) is his semi-subtle way of resisting Kanna's Shipper on Deck attempts to pair him off with Ichika
Tetsuro, Kanna, and Mio's appear to be playing I Want My Beloved to Be Happy when they're actually playing "Push 'em together to make them figure out that I'm the one who's really compatible/cares for them."
Ichika's enrollment as a transfer student is due less to Compulsory School Age than to her desire to stay close enough to Kaito to ensure the healing nanites finish their job.
At the climax of the show, Ichika needs to reach the place in her memory to find evidence of previous contact between aliens and humans. Along the way, she and her friends are attacked by alien rescue drones, which are eventually beaten off by the Men in Black—an organization of which Remon, Ichika's closest friend, is a member. But the Men in Black are implied to be the same organization as in the film of the same name: formed with the purpose of investigating and monitoring alien activity on Earth. In other words, the existence of the Men in Black itself implies that aliens have already made contact with humans. So why couldn't they just submit as evidence whatever prompted the creation of the Men in Black, rather than needing to pursue the lead inside Ichika's memory specifically?
