This is my explaination for the connections between

Higurashi and Umineko

1) Rika/Witch Bernkastel/Lady Frederica

Hanyuu was part of a demon race that moved into Hinamizawa long before Rika's birth. Her demon clan was going to be thrown out of the village, but was stopped by the Furude Heir, Riku Ferude, who fell in love with Hanyuu. They had one daughter, Ouka Furude, who strongly resembled Rika. The villagers got fed up with the demon's residing within their village and began rioting. Hanyuu offered her life as a sacrifice to calm the villagers. Hanyuu ordered her daughter Ouka to be the one that killed her, which resulted in the first Watanagashi Ceremony. This gave Hanyuu godly powers as a spirit. Many years later Hanyuu, seeing a resemblance to her daughter, took interest in a newborn Rika Furude. Hanyuu attached her spirit to Rika making them inseparable. Hanyuu did not want her new "host" to become evil like the people in her past , so she removed all darkness within the young Rika and, using her godly powers, banished it to an alternate realm, the realm of "Umineko". The darkness soon manifested into a being identical to Rika, who called her self Frederica Bernkastel. The name Frederica was taken from "Furude Rika", the Japanese pronunciation of Rika's full name. Bernkastel may have come from Rika and Bernkastel's stated love for wine, since Bernkastel is a famous wine-making country in Germany. Since Hanyuu and Rika were spiritually connected, all of the, albeit small amount, of darkness within Hanyuu was also banished. This manifested itself into the being Featherine, who vaguely resembles Hanyuu. The smaller amount of darkness within Hanyuu explains why Featherine is less sinister than Bernkastel. Featherine's name came from the two kanji (Japanese symbols) that make up Hanyuu's name which translate to "feather" and "in".

Being removed by Hanyuu, both contained small fragments of Hanyuu's power, or "magic" as they call it. Bernkastel, using her magic, created a "board game" of Rika's life. Bernkastel hates Rika for removing her, which means that Bernkastel can never be whole. This is also why she shows little to no emotions throughout the series. Bernkastel wants Rika to suffer, so she created the "board game" so she can control Rika's life, which results in Rika's countless deaths. Rika is aware of this and has even had the rules of the game explained to her. The rules are: X- Someone must be infected and go insane. Y- Takano and Jirou must attend the Festival. Z- No one besides the Furude clan can enter the sacred shrine. Bernkastal is powered by the bad memories of Rika's "lives". Memories such as her friends going insane, the deaths of her friends, and most of all the death's of Rika. Each "life" Rika goes through becomes a tile in Bernkastel's "board game". Featherine, being connected to Hanyuu, undecidedly gains power from Hanyuu's suffering. Suffering caused by helplessly watching all of her loved ones die over and over. Over time, the good memories from Rika and Hanyuu's lives manifested itself into a being that called itself Frederica (also taken from "Furude Rika"). Having fragments of both Rika and Hanyuu, Frederica is identical to Rika while also containing bits of Hanyuu's power. This allows Frederica to wander through time and dimensions.

2) Takano/Witch Lambdadelta

Frederica often watches Rika's "lives" while wondering through dimensions. Frederica is fond of Rika and Hanyuu for giving her such good memories along with godly powers. She notices that Takano Miyo is one of the main causes of Rika's suffering. Frederica wishes to help Rika in anyway she can, so she decided to take action. Frederica entered the most recent world and travels back about 20 years to the day that Takano's parents were killed in a bus crash. Originally, Takano (whose original name was Miyoko Tanashi) was at her friends house when her parents were killed. She was then put into an orphanage. Takano and the other orphans were constantly abused, which drove them to escape. Takano called her fathers old Doctor, Hifumi Takano to save her, but she and her friends were caught before he arrived. Takano was forced to watch her friend suffer strange forms of torture before she was saved by Hifumi, who adopted her. That is when she took the name "Takano". Due to her twisted past, Takano was driven to do the horrible things she did. Frederica knew the course of the events. She gave Takano two choices: 1. Go to her friend's house and suffer or 2. Go with her parents and live a happy life. Takano, of course, went with her parents who chose to take a different bus which didn't crash. This is why Takano (now Miyoko) was no longer the antagonist of the series. Throughout Rika's "lives" the events of Takano's past repeated and her darkness was "recycled". Now that Takano's past was changed, her darkness was left aimless, drifting between dimensions. It eventually manifested itself into a being identical to a young Takano named Lambdadelta. Bernkastel was angered by the tampering with her game, and how she was unable to stop it. She decided that she needed more "players" in her game. She takes the wandering Lambdadelta and gives her a proposition. She tells Lambda that if she plays her game, she will make her a powerful witch. Lambda accepts and is made a witch. Bernkastel, despite being almost emotionless, still needed a companion (other than Featherine). She adds a few attributes of Satoko, her best friend, that she recalls from her dark memories. These attributes include Satoko's sinister laugh and love of traps.