Alright, halfway point!
Setsuna meets with Karen and Sara behind the Urashima shrine. They ask him what he thinks of Rinne, but he says he’s more focused on his own issues right now. Namely his missing memories. Sara suggests, to Karen’s annoyance, that Setsuna go on a date with Rinne and maybe then some of his memories might start to return.
That night Setsuna flips through his journal and reviews what he knows about his time on Urashima Island. He feels that the names “Setsuna” and “Rinne” are key to learning his true identity, and that there also things relevant to his situation which are hidden inside that shack in the cave on the beach. The thing is, how can he get in there without Rinne (or anyone else) finding out?
Then Rinne enters his room and asks if she can sleep next to him. Sara did it so she can too, right? The scene is initially rather awkward, but the two quickly become comfortable with each other.
In the morning Setsuna and Rinne have breakfast together, and Rinne invites Setsuna to spend the day with her. As a date-that’s-not-a-date, of course. ;D Rinne dresses up nice and puts on a little make-up, while Setsuna… just wears his usual clothes. I guess all he really has is the one outfit. As they leave Rinne’s mother Kuon watches them go, and while she initially appears happy to see them together, her smile quickly turns to anger for some unknown reason.
Rinne and Setsuna bike to the bowling alley where Rinne beats him at a game of 10 pin, which means Setsuna has to treat her to something delicious. Near the end of the day they sit on a fence by the beach and watch the sun set. Setsuna teases Rinne for taking so long to get used to being back outside like a regular person, but when she protests he quickly gives her credit where it’s due.
And I think this is what I like the most about Setsuna and Rinne’s relationship: they get along really well and they can tease and flirt with each other, but they’re both honest and loyal people. Setsuna knows he can tease Rinne but if she becomes hurt then he reverts to his “true self” and is quick to reassure her that he still cares.
The next day Sara and Karen reconvene for a meeting. Karen muses that Setsuna and Rinne had such a good time on their date that 
they’ll probably start dating now, but Sara is upset and says that can’t be allowed to happen. Rinne is from the present and Setsuna is from the future… except Rinne too came to the island 5 years prior (supposedly), so maybe she’s from the future as well? Or the past?
But this whole thing is stupid, IMHO. If Sara didn’t want Rinne and Setsuna to become close enough to take their relationship to the next level (or two), why would she encourage them to go on a date? Did she not remember before her morning meeting with Setsuna that he and Rinne are from two different time periods?
Sara drags Karen over to the Ohara household to speak with Setsuna and Rinne, except it appears that they’re away. Karen wants to leave, but just then Setsuna and Rinne show up – wearing his and hers items from the catalogue Sara had been looking at earlier in the episode!
Inside everyone sits down in the living room together, and Sara asks Setsuna and Rinne point-blank if they’ve had sex yet. Sara is relieved when they tell her no, and cautions them against anything romantic, even having feelings for each other. Failure to heed her warning may cause a “space-time shockwave” which could have severe consequences for everyone.
Later in the day Rinne and Setsuna are down on the beach again. Rinne teases Setsuna about kissing her as a prize for a game they’re playing, but when he don’t respond she pretends to casually dismiss the idea. They chase each other, but the game ends when Rinne says she’s not ready to lift the veil on her secrets (in reference to the shack on the beach and what it contains). Now I’m more eager than ever to learn what’s inside it.
In the morning Setsuna wakes before Rinne and bikes to the island’s convenience store to buy something for Rinne to cheer her up. Meanwhile Karen meets with the young officer at the police station and they joke about her confrontation with her father during their fake wedding. When the young man says he hasn’t given up on marrying Karen, she instead tells him about her three friends from school, “A, B & C.”
There’s some back-and-forth sneezing between Karen and her friends (the joke being that you sneeze if someone is talking about you), and then Setsuna walks into the police station to get a quick break from the heat. The three of them start discussing Rinne and the island’s old legends. The young officer reveals that each of the three main families on the island have their own version of the legend. Apparently the “real” ending of the legend is that Rinne is reincarnated, and happily marries another man. When she learns of Setsuna’s existence she becomes filled with despair and kills herself by throwing herself off a cliff into the ocean.
The young officer figures that Rinne probably knows this version of the island legend, even if she hasn’t ever mentioned it to Setsuna or anyone else. After all, her father Norimasa Ohara is the person on Urashima who was responsible for collecting all of the legends together.
Setsuna rushes home but Rinne is already gone. He tries asking Kuon where her daughter is gone, but she’s only interested in learning whether Setsuna and Rinne have had sex yet. -_-;
Setsuna eventually finds Rinne down on the beach, and she’s in a truly dark mood. She tells him she can’t enter the shack without him, so they travel to the shack together. I didn’t think we’d get to see this scene within this episode, so yay for great pacing!
Rinne reveals the truth: Setsuna isn’t the “real” Setsuna; there was another young man with the same name who came before this Setsuna. Rinne however is determined to forget the past, saying that this Setsuna is hers, regardless of who came before him.
Setsuna and Rinne break into the shack where they find a bed, a desk and a bookcase. Strewn around the room are lots of old, dusty books. Rinne’s memories return to her: the original Setsuna used to stay in the shack at night and Rinne would visit him, then sneak back home before the tide came in. However one night she waited too long and the tide trapped her in the shack. Her father panicked and started looking for her. He found Rinne and Setsuna together in the shack, and accused Setsuna of stealing Rinne away. The two men fought and Norimasa pushed Setsuna into the sea. Just then the sun came up over the horizon and Norimasa died when the sunlight bathed his body – he had soot blight syndrome, just like Kuon does. Rinne dove into the ocean to try to rescue Setsuna, but woke up alone in the Urashima hospital. The original Setsuna was never seen again.
Then this second Setsuna washed up on the beach, and his presence helped rescue Rinne from her nighttime lifestyle. He encouraged her to meet new people and be herself, and not always hide away in the darkness.
Naturally this new information just invites more questions. Is this second Setsuna a reincarnation of the first one? Are they both from the future? Is this Setsuna’s arrival on Urashima a second chance for Rinne and Setsuna to fulfill the ancient legend from the past??? So many questions!!!