If something radically altered your DNA, the first place the changes would show up would be at the site of a wound, where cells are dividing rapidly and new tissue is being produced. What's the first part of William Birkin to mutate dramatically? His right arm, which was riddled with bullets during the laboratory break-in. In addition, Birkin only changes forms after you fight him; he gets more alien every time he heals.
If you watched the cutscene where mutated William, you can see that we saw three of them getting killed, but there were four of them. The one who escape was Hunk.
Watch the opening cutscene as Claire rides into town. The first living residents of the city in the cutscene are...some rats crawling along the top of some crates. Later in the cutscene where Annete Birkin describes her husband's death it's shown that the rats, as the initial carriers, helped spread the infection around the city.
Why does Wesker have a picture of Rebecca Chambers? In Resident Evil 0, he apparently recognizes her as one of the newest members of S.T.A.R.S while searching that picture, and leading an investigation of the first game.