As for Rika and Frederica they are totally different. There is a message she left in Higurashi for this issue.
Quote:
I am who I am; Frederica Bernkastel.
Furude Rika and Frederica are different. Shame on you if you thought so.
My age? I've gotten bored with it, so I've quit counting.
Huh? Are you speculating that the real identity of the Oyashiro-sama is me?
Giggle giggle. You are so insolent.
The Oyashiro-sama is the Oyashiro-sama. You want me to introduce it to you? It's rather shy.
It gets frightened easily so don't scare it, okay? However, it seems that you are the one that's scared.
Giggle giggle giggle...
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EDIT: Well I guess if you didn't notice Furude and Furudo are a play on words. It looks like to me that they're engrish for the "Fred" part of Frederica's name. It ends up being "Furude" or "Furudo". Then you just add on " the Erica" part of her name for Erika or Rika and you get the full name for Ryukishi's characters.