Billy knows more than what he told RebeccaWhat happened to Billy Coen in Africa (interestingly enough, people think the protagonist in RE5 is Billy, though clearly it's Chris, now having seen the new trailer), and what did it have to do with the mother virus? (I initially thought that Billy's exclamation in the factory was simply an RE2-style plot dodge; it's assumed that the player knows what a given virus is by now, if only from files, so the character does too. However, Billy says "mother virus," and no file in RE0 mentions that. They're all about the Progenitor.)
Wesker and Birkin just pretended to be rivals in order to prevent Marcus from getting suspicious and/or paranoid about them.One of the diaries in Resi 0 notes that the two are very competitive, yet they seem to be perfectly willing to cooperate in containing the T-virus outbreak during the game itself, and Birkin's letter to Wesker at the end of REmake is pretty friendly. Since they apparently also cooperated on Marcus's assassination, it's apparent they intended to usurp his position from the beginning, and pretended to be rivals to prevent the idea from ever entering his mind.
Umbrella builds many of its laboratories in the same style.It would explain why Rebecca and Billy can visit an area that looks like the entrance of Birkin's lab in Resident Evil 0.