Sherry and Jake can't be separated, since the game will be cooperative at all the times. They could take different routes for a brief section, but not like that.
Sherry has been hinted to have quick-healing habilities so the blood probably doesn't imply any serious/permanent damage.
It is entirely possible that they can be separated since the outbreak in Edonia takes place six months before China. Chris and Piers will be separated also for a short period of time before the outbreak in China. When I saw the scene where the J'avos separated Jake from Sherry, my immediate thought was that they were now captured by the US government and/or Neo-Umbrella and they would find a way to escape and reunite before/during the China outbreak. About Sherry bleeding, I think that is from when the Ustanak bitch slapped her (lol) from the 2nd trailer. After Jake deals with Carla Radames when she tells him about his father, Jakes sees that she is bleeding. Isn't it rumored that sherry has some type of accelerated healing ability due to the G-virus? I think this is when we'll see what her abilites can do.