This series has always been awash in contradictions, and the finale was consistent with that, right up the end. This last episode did a fine job of helping us feel the pain the twins were feeling. For Sora, it's simple - she's been living in a sheltered fantasy world for her entire adolescence, with Haru as the only focus. She can't understand why things aren't as obvious to Haru as they are to her. For him, things couldn't be less simple. He's both rational and a functioning member of society - things Sora is not. Haru is both intellectually and emotionally horrified by what he's doing with his sister. Yet he's also a sexually charged teenager, and is truly in love with his sister. As Nao says, you can't choose who you fall in love with.
Throughout the final drama, it's Nao who shines. It always seemed very possible that she - despite having the most legitimate grievance - would be the most understanding. She loves Haru, but she also loves both siblings as true and dear friends. She understands loneliness and being scorned better than anyone in the group, and she feels the pain Haru is suffering. She wants them (especially him) to be happy. Though she didn't "win" in the romantic sense, Nao transcended the limitations of her hard life and was truly noble in the end.
As for the end, it's an ending where you can basically believe whatever you choose to believe is the truth. The symbolism of what happened is more important than the cold hard facts. I think the director was trolling the audience a bit - intentionally dropping conflicting hints in an effort to leave things up to interpretation. Perhaps more importantly, in both ends Haruka and Sora are together - whether in death ("In solitude where we are least alone") or abroad somewhere, building a new life. It was a very effective final episode, either way - suspenseful, painful, challenging and thought-provoking.
I would credit this series as doing a better and more interesting take on the omnibus format than Amagami SS. While in that show it was largely a gimmick, here it served the larger story, helping to reveal facets of Haruka and Sora's character, each preliminary arc a different window into who they were. The Nao arc, especially, flowed seamlessly into the Sora arc - there may not share an exact continuity but the emotional tenor of the two is in perfect concert.
After watching the series and playing the VN.. some speculations for the bad and good ending.. (some might contradict some points)
Some below are gathered from other users, so I don't take credits for everything.
Reasons why they lived:
According to VN, Sora saved Haru.. they went to Europe for vacation, sent a text to Kazura.
According to VN, Sora can swim.
Akira noticed someone was outside her house.. and when she was shown in the anime, it was the same scene as Akira's arc, and this day she just performed the ritual dance.
The bunny might be very popular and can be bought elsewhere.
According to Omake ED, Nao might have found them and saved them, and she does seem like one who would leave them alone after making sure they are fine.
According to the anime OP, Sora and Haru were in water (where they were drowning) but a sudden light from above brought them upwards, this might be of the goddess (Sayuri Hime) of the lake which saved them.
Since they planned on leaving, they wouldn't bother fixing up the broken rooms, making the bed and such.
Kazura was the only person with a cell phone, besides the twins and her dad, that's why she got the text. Nao only talks through local phone.
I personally believe that this anime is made for a happy ending, just my thought though. We just might be over thinking too much.
Reasons why they died:
When Sora and Haru were running into the lake, Sora clearly showed signs of drowning before Haru got to her, and Haru definitely thought maybe it was a good idea for them to die together.
In the VN, Haru and Sora had the same idea when they were drowning (to die together)
In Solitude, Where We Are Least Alone. Death is their only solitude, if they want to be together forever with an incest relationship. To a place where nobody else can get between them, to somewhere they can be least alone.
Nobody would be able to find Sora and Haru if they drowned into the lake, there was no way for anyone to tell someone drowned in the lake by looking from outside the lake.
The dead trees below the lake resembles death.
After the drowning scene, when Haru wakes up, he saw the Milky Way, it represents road to heaven in some myth.
The broken doll is the biggest evidence they died, since the doll in the train scene is completely perfect, and that the doll is Sora's mom memento, it would lose its meaning if they just get a new one.
All the characters looked somewhat unhappy after the incident, as if they knew about something Prez didn't know about.. especially Akira, if the characters goes the way they did in the other arcs, she is most likely the one who created the mail, to prevent others from being unhappy. (She would be like in her own Arc, trying to prevent others from being unhappy and being all lonely herself.. etc)
Also, since Prez is the one who led to all this.. and despite her personality, others might keep this truth from Prez to prevent her from doing anything reckless..
The train scene is a metaphor of road to heaven.. there was nobody on the train (and again there was nobody on the train when they came), no person announcing stations, and Sora was wearing a white ribbon which she never had before.. Also the scene outside changed from dark to bright all of a sudden, as if Earth reached heaven.
Remember Haru received a text from Sora? and Haru had the phone with him when he was looking for Sora, which means they both ran into the lake with their phones, thus they cannot send text to Kazura unless they buy another one, but the village is not a modern city and doesn't have cell phones, I doubt they had time to buy a new one before reaching their destination..
The text Kazura received had no date on it.
In the Anime, Haru clearly stated they had no money left.. how would they be able to travel? And Sora clearly will not accept that they get separated.
Sora never answered when Haru asked if they are alive.