Question: In the scene at the House of Blue Leaves, (right after the Bride kills GoGo), O-Ren is holding Gogo's small sword. She begins to unsheathe it before stabbing it into the railing. What was the point of it? Was she upset because Gogo died, or was she contemplating suicide in lieu of facing the Bride?
Question: If Bill is behind the death O-Ren's parents, did she know? If so why didn't she go after Bill?
Answer: There is nothing in the film that states or even particularly indicates that Bill is somehow behind the deaths of O-Ren's parents. The only explanation we get is that their death was ordered by Yakuza boss Matsumoto, who brought in the thugs that killed her father. There is a semi-popular fan-theory that the man in white (Pretty Riki) is actually a young Bill, but to my knowledge, this was never confirmed by Quentin Tarantino. (In fact, according to the Kill Bill wiki, Tarantino actually denied they were the same person, but I can't find the source for that.) So there's literally no reason for her to go after Bill. As far as she (and the audience) knows, he was uninvolved in their deaths.
Question: Why are there 2 swords on the plane with the bride?
Answer: Because they are being carried by the other passengers.
Answer: There are more than 2. They are positioned similarly and look similar to The Bride's. So, Tarantino is saying The Bride isn't the only passenger with a kill list. This is where Tarantino reminds us that this is an allegory with The Bride representing all good people seeking revenge against the evil people who wronged them. A common theme in Tarantino films.
Question: Why did Matsumoto have O-ren's parents killed?
Answer: The film does not explain, but O-ren's parents must have been involved in some sort of shady business dealings to have incurred the wrath of Matsumoto. When he is killed, O-ren's father is wearing the uniform of a United States Army Sergeant Major (pay grade E-9), which is the top rank of an enlisted man. He must have been working with Matsumoto in some sort of illegal smuggling ring that involved international connections through the U.S. Army that went bad, or maybe O-ren's father wanted more money and he was in the way, etc.
Question: Does anyone know what happened at the Bell household, after the Bride disposed of Vernita? I'm also curious as to what happened to Sophie, after her rough night.
Answer: For years there's been a rumor of a third movie with Sophie and blind Elle teaming up for revenge on the Bride.
Answer: It's never been stated what happened to be Bell household. Re Sophie, towards the end of Vol. 1 we see Sophie talking with Bill and if you listen to what Bill is saying and how he is articulating his speech you could make the assumption that he is really angry at Sophie for giving the bride the information rather than dying. My assumption would be that after Sophie told Bill everything about the Bride he would have killed her.
Question: Why did Jasper need to pay Buck to let him rape The Bride? Why couldn't he just walk in and do it for free?
Answer: Buck is wearing scrubs in the scene, so he probably works at the hospital. (A Kill Bill wiki says that he is a nurse.) Jasper is paying Buck for access and to not be disturbed while he commits the rape.
Answer: To be honest, it's a mix of both. O-ren and B were close in the hit squad. B knew O-ren's backstory, suggesting a shared past. They had common interests, spoke Japanese, and used samurai swords. O-ren confided in B and may have been her squad member. O-ren shared her shame with GoGo, indicating a deep bond. Bill supported O-ren's Tokyo takeover, indicating their closeness. Their shared dialogue suggests an inside joke. O-ren contemplates suicide for betraying her friend and killing her child. She feels remorse for failing to defeat Beatrix and cares for GoGo, who died protecting her. When the 88's arrive, O-ren resolves to fight for honor and avenge GoGo. She knows Beatrix will defeat the 88's, so she prepares for their upcoming battle.