Unfortunately, this is no neat wikipedia page about Rika's identity problem that I could link. So I made this. I hope it works.
Rika's identity crisis is a complicated but important facet of her personality and she is coming to Destiny Strings with overcoming it in mind. It might seem strange at first glance for Furude Rika to have a persona named Furuderika (pronounced quickly, it slurs to "Frederika"), but that is just what Furude Rika is to this girl; a persona. She still has trouble identifying with actually being Furude Rika, instead often thinking of herself as "Frederica Bernkastel, the witch who goes between worlds."
I prefer Furuderika as her persona as opposed to Frederica Bernkastel for one major reason: While it may seem like Persona=Character in calling her persona Furuderika, it would actually be closer to Persona=Character if Frederica Bernkastel was her persona's name. I also hope it would make a good CR conversation starter and help force Rika to level with her new friends about her identity problems and sort them out.
Below is just some additional information that the Wiki lacks, for further explanation on all of the "Bernkastel" nonsense, then a description of her canon worlds.
Maybe the hardest and most insane thing to understand about Rika is "Furuderika Bernkastel". If you've read/watched Umineko than you probably know Bernkastel is a cat-tailed witch that likes to clean the tea out of cups and stare around blankly. And then sometimes troll people.
In Higurashi, Bernkastel has two major instances of being mentioned. The first is in the poems she writes; The arcs are usually accompanied with a sad and mysterious poem written by Frederica Bernkastel. The second is in Rei, and is the biggest connection between Rika and her "split personality.
To start, you need to keep in mind that Higurashi is about world jumping not time skipping. There is some time travel involved in the sense that Rika goes to a time before when she is supposed to die, but every time she dies she is sent to a new world rather than going back in time in the world she dies. Proof of this is shown due to the fact that Shion and Rena both have canon appearances as adults, and there is a tip about an interview with Keiichi. In all of these instances, time has progresses passed Rika's death, even though she does beat her fate eventually in canon. This means that Rika left these worlds where she died and time continued to pass in them.
So how does Rika World Hop anyway?
The key is Furude Hanyuu. It's suggested that both Hanyuu and Rika hold some power, which Hanyuu uses to create the world hopping. When Furude Rika dies in one world, Hanyuu gathers up the memories that Furude Rika held and sticks them in a Furude Rika in another world.
Naturally, this leads to a personality swap, which is where some distinctions will be made to avoid further confusion.
The Rika that has no memories of the cycle of dying is called "Furude Rika". She's a clean slate whose personality is of an innocent child. This is the girl that the other people of Hinamizawa know.
But when the memories of other worlds are put in her, she becomes "Frederica Bernkastel". Rika picks this name for herself, combining "Furuderika" into a Western name and then stealing "Bernkastel" from a brand of wine her father drinks. Rika says that she only feels alive and pain-free when she is drunk on the wine, so sarcastically says that "she is the wine".
Frederica Bernkastel is not, however, the witch from Umineko. Bernkastel in Umineko is cruel and sadistic and ruins people's lives for fun, which is certainly not the personality of Rika. Even Frederica Bernkastel, Rika's dark side, would never promote cruelty. She's trying to get out of the cruelty.
The distinction between Frederica Bernkastel and plain ol'Bern is made in Rei. In short, once Rika has defeated the cycle of death she continues to hold the "if I die, I can try again" mindset. This is definitely not a human mindset, at least, not a normal or healthy one. We see a glimpse of just how unhealthy this is in Minagorashi-hen, when Rika nearly commits suicide so she can go to a world where Satoko isn't abused.
In Rei, Rika realizes that she's developed this unhealthy tendency to leave worlds and look for happier ones in a non-human way. Like a witch, almost (FORESHADOW?). It is at this point, when Frederica Bernkastel decides that she wants to live a normal happy human life, that "Frederica" and "Bernkastel" split. Frederica accepts that she has found her final world and that the next time she dies, she is dead for good. And slowly, "Frederica" deconstructs back into a happy little "Furude Rika", who no longer has to suffer but can enjoy her life.
And Bernkastel floats off to go troll the hell out of people.
It can essentially be seen as all of the cute happy thoughts going to Frederica and all of the batshit insane going to Bernkastel. And then Bern's crazy multiples and triples and it just gets really bad.
Anyway, for the purpose of this Furude Rika...
I generally play her as "Frederica Bernkastel". She has not found her happy ending yet and continues to travel between worlds, so still retains both the "Frederica" side of her personality and the "Bernkastel" side. She is not a witch though. Frederica Bernkastel is just a girl with more memories than she needs.
WORLDS SHE HOPS TO
Rika is the one character in the series that keeps her memories in every world. She's been to all of the worlds. She is essentially a huge series spoiler, so in order to fully understand her, you need to jump into some spoilers.
THE FOLLOWING SPOILS THE ENTIRE SERIES. This are just little summaries of things I vaguely touched on in her main history.
In Higurashi, there's a parasite that affects a person's brain called the "Hinamizawa Syndrome", simply because the parasite can only survive in the geographical conditions of Hinamizawa. This parasite affects every villager, but doesn't harm them until they leave the village. At that point, when it leaves Hinamizawa, the parasite becomes active. It starts by making the person infected paranoid, so much so that they often end up becoming homicidal, and then it causes them to become "itchy". They itch themselves (usually their throat or wrist) and become convinced they have bugs under their skin. When they start to bleed, their paranoia causes them to see the bugs and itch more to get them all out. In the end, at this final stage of paranoia, they scratch an artery and bleed to death.
There is no cure, but the Irie Clinic is researching a medicine that halts the progress and keeps you from being paranoid and homicidal (as long as you take your meds). In order to use this, you need to blood of the "Queen"; the queen is the only one in Hinamizawa who is not driven crazy by the parasite. But when she dies, everyone infected, regardless of whether or not they left Hinamizawa, goes crazy within 48 hours. The Furude head of house is the Queen, and the latest in the bloodline is Rika, so her blood is needed. Houjou Satoko is very infected (at the "final level" before suicide), so takes the medicine every day (but she thinks they're vitamin injections). This gives Rika easy access to the 'cure', and because she's so heavily involved, she knows everything there is to know about the parasites. No one else but Dr. Irie and Nurse Takano know about it yet (Okay, and Tomitake and Takano's goons...)
Worlds Rika Visits
Onikakushi-hen is the first story arc. In this arc, Maebara Keiichi leaves the village for a funeral. When he comes back, he learns of a case five years ago in Hinamizawa where a construction worker building a dam (that would put the entire village under water) was brutally murdered and split into five parts. "They still haven't found one arm, have they?" is the quote from a free lance photographer, Tomitake, that inspires Keiichi's paranoia. He becomes convinced that his friends from school, Ryuuguu Rena and Sonozaki Mion, are behind the killings. This arc shows you everything through Keiichi's eyes, so they appear scary, but should you listen to the dialog, you'll find it's all friendly and concerned dialog that Keiichi is mishearing. In the end, he kills Rena and Mion, then scratches out his throat and dies in a telephone booth.
In Watanagashi-hen, you meet Mion's twin sister Shion. She's very sweet and kind to Keiichi, but in the answer arc, Meakashi-hen,you learn that she's flirting on purpose to try and get Mion (who actually has a crush on him) to take action in winning Keiichi's heart when she actually has 'competition'. Watanagashi-hen involves Shion and Keiichi sneaking into Oyashiro-sama's shrine with Takano (a nurse at Irie Clinic) and Tomitake. They become "cursed" for what they did. Takano and Tomitake die on Watanagashi due to the yearly curse while Shion and Keiichi are haunted. Anyone they tell about what they did is killed and they believe it is leading up to them. Near the end of the arc, Keiichi realizes that the "Shion" he is talking to is behind the murders because of her wording of sentences, and confronts her with Rena (Rika and Satoko have become victims at this point). They think Shion is Mion and Shion eventually knocks Keiichi out, then after he recovers from that, shows up and stabs him.
However, in the answer arc, it's revealed that it was Shion committing the murders, and that she was using her twin's identity. An important Rika moment in this arc is that Rika recognizes Shion for having the Hinamizawa Syndrome. She takes some of the medicine for it and tries to inject it into Shion, but Shion is so paranoid that she thinks Rika is trying to poison her. Rika is the Queen, and essentially is the parasite, so when Shion injects the medicine into Rika instead, it had a very negative effect on her. Since Rika has clearly done this in other worlds, she knows that Shion intend to torture her before she dies, so commits suicide.
Shion did all this for love, in a twisted way. The boy she loved, Houjou Satoshi, was supposedly "demoned away", and she thinks the house heads in Hinamizawa are the ones behind the mysterious deaths. So her original plan is to kill everyone involved in Satoshi's death. She 'wins' and then falls off the balcony of her apartment and dies.
Tatarigoroshi-hen involves child abuse (it's probably the most depressing too). Houjou Satoko's parents died a while ago, so she's been living with her uncle and aunt. But after her aunt was killed by the curse, her uncle rarely comes home. In this chapter, he comes back, so Satoko has to go live with him again. He severely abuses her, mentally and physically, and has her convinced that she can't tell anyone or get help because this is a "test" to make up for all the trouble she caused her older brother,Satoshi. If she doesn't do what he asks, he's threatened to burn down Satoshi's bedroom, and to Satoko, that will be the final sign that her brother can never come home. It is Rika that explains the situation. Keiichi is the lucky infected one in this arc, and goes out to kill Satoko's uncle. He ends up dragging Satoko around for a while, and they learn that Dr.Irie has died from an overdose on sleeping pills. They go to the shrine, because Satoko needs new clothes and they're at Rika's house, and Keiichi finds Rika, dead and disemboweled at the foot of the shrine. Satoko comes back, assumes Keiichi did it (then again, the genius boy did pick up a bloody ax to swing at some crows after Rika's...er...I'll shut up) and shoves him off a bridge. He wakes up after being KOed and learns that there was a "volcanic gas" eruption in Hinamizawa and that every villager was killed. The arc ends here.
An important note for Rika is that she considers this world to be the most hopeless and depressing. She hates to think about it because Satoko is abused. Though she hates all of the worlds where people die, this is probably her "least favorite".
Himatsubushi-hen is a prequel, and happens five years before the start of the other arcs, which is also before the curse begins. Akasaka Mamoru comes to Hinamizawa to investigate a kidnapping and meets younger Rika she's about 6 or 7 at this point). He learns of the dam project, which would put Hinamizawa under water, and how the villagers are protesting. "Dark Rika" first appears in this arc, warning Akasaka to go back to Tokyo. She also tells him that the dam construction will be stopped and that, in five years, on June 19, she'll be murdered. He doesn't believe any of this. Later in the arc, she cuts all of the telephone wires so he can't call home, saying that if he did call home, he'd be very sad. When he gets back to Tokyo, he learns that his wife has died, on the exact night that Rika cut the wires, and before she warned him to go home. Five years later, all of the predictions Rika made are confirmed, and Akasaka feels very guilty.
Tsumihoroboshi-hen is next. In this arc, Rena becomes slightly aware of the syndrome, but she thinks it is because of aliens. Naturally, no one wants to believe her. She realizes she has the syndrome and will die soon, so holds the school hostage and demands that the police find a cure. In the version of this arc you see, Keiichi remembers the first arc where he went crazy and becomes determined to help Rena before she makes the same mistakes (Rika forgives Keiichi for killing everyone as well). Rena realizes she's hurting her friends and stops due to Keiichi's efforts,and Rika realizes (slightly) that fate can be changed if you work together; In the manga-only arc, Yoigoshi-hen, Rena burns down the school and kills everyone in it. Either way, the Hinamizawa Disaster comes, poisonous gas goes everywhere,and everyone dies anyways, regardless of whether or not Rena burns the school down.
There is also the anime-only arc, Yakusamashi-hen, where Satoko catches on to the fact something is wrong and tries to save Rika. When the night that she will be killed comes, Rika has Satoko hide and allows herself to be taken without protesting. This sacrifice suggests that, in past worlds, Satoko has possibly protested Rika's being kidnapped and been killed to be silenced. Satoko does some running around, gets knocked out, wakes up and finds the village after the disaster. She freaks out and goes into mental shock, so cannot talk or interact,just sits in the hospital. Before the police can get answers out of her, one of the nurses puts bubbles in her IV and she dies when the bubbles enter her bloodstream.
There are a few other arcs, but these are the only ones my Rika will acknowledge as worlds she's visited.