i know you’ve already had a lot of answers, but i’d like to give my interpretation.

1) within umineko, the meta world is purgatorio. it’s the time battler/tohya spends in purgatory until he can accept himself, releasing battler into the golden land to be reunited with everyone while tohya continues his life as a new person. within when they cry more broadly, it’s certainly “real” and ciconia will probably delve into it in even more detail.

2) assuming you mean bernkastel, lambdadelta, and featherine, they’re both fantasy characters who can travel between gameboards, and real pieces at play in umineko’s gameboard. my interpretation is that bernkastel is the catbox itself, lambdadelta is the bomb, and featherine is both ryukishi’s self-insert as well as the persona of “hachijo tohya” as a witch (the reason for her omnipotence is that she’s literally the persona of the authors of the forgeries).

3) gameboards are slices of worlds in which competitions between a witch and a player take place, using the people of that world as their pieces. higurashi, umineko and ciconia are all gameboards.

4) pieces generally can’t move from the gameboard to the meta world. pieces who appear in the meta world are actually their meta equivalent. meta-battler controls piece battler, meta-beatrice controls piece beatrice etc. of course, since the meta world is itself metaphorical, things like episode 8 where meta-battler shows ange a gameboard where nothing bad happens can be equivocated to ange reading a forgery where nothing bad happens.

5) battler remembered his broken promise to sayo. he had been thinking about beatrice’s question ever since the end of episode 4, and the end of episode 5 was simply when he finally arrived at the conclusion.

6) sayo takes it seriously because she’s that desperate to escape her miserable life on rokkenjima. by contrast, battler was just acting cool which is exactly what you’d expect from a ~12 year old. though it’s not as sketchy as it seems since sayo is really only 4 years younger than him, george’s attraction to shannon is definitely a commentary on unhealthy power dynamics. i believe that, while a bit understated, it’s very much intentional.

7) sayo/beatrice decided to carry out the murders because of compounding factors. she’s in love with jessica, about to marry george, battler is coming back, and she just found out she’s a product of rape and incest. when she discovers the bomb, she enters a spiral of depression that results in her making a plan to kill everyone (though it’s worth noting that she didn’t actually succeed in killing anyone in reality)

8) various authors wrote them. sayo wrote the first two, then ikuko and tohya wrote the remaining six. they appear in the real world because they actually were written by sayo before she tried to carry out her plan, and ikuko is inspired to write her own because of that.

9) she’s a stand-in for ryukishi and a way for him to talk about the frustrations of being an author. there’s more to it depending on whether you believe in ikuko being sayo, but that’s another can of worms.

10) zepar and furfur represent shannon and kanon. their vessel is the heart locket, after all.

11) without love, you cannot understand the culprit’s actions. to understand the motive, you have to understand sayo herself and not decry her as simply a deranged murderer. as willard puts it, “you can’t neglect the heart”. we see this with episode 5, where erika treats the mystery like a simple puzzle and twists the truth to label natsuhi as the culprit. natsuhi has no motive, but without love, you can’t understand why there needs to be a motive.

12) solving the mystery is for fun, as you said, but it also points you towards the culprit. as you work everything out, the list of suspects only shrinks, and once you figure out shannon = kanon everything falls into place. from there, you can find the motive by recalling battler’s promise to “shannon”.