Don't know if you saw the dialogue after the credits and the text that rolled before it, but Ocelot says the real BB is creating the true outer heaven, meaning its the clone you kill in MG1 and the REAL BB shows up for MG2 in outer heaven. During the text it says BB Phantom is killed by David, meaning the real BB shows up for MG2.
I agree with the Quiet part, I also think she was the most interesting part of the game, sexualization aside, lol. As for her, it can be assumed she died after saving Snake, she had the english strain of the virus, meaning when she spoke english she would get infected and infect anyone else around her that spoke english. Which is why she disappeared. If you recall, anyone infected ended up dying if untreated, Quiet was not gonna get treated so she's pretty much dead.
In the grand scheme of the series, this was actually a pretty good story and definitely tied together some things that didn't make sense and set up the rivalry between the characters. Was disappointed we never got to see Solid Snake though

lol.