Question: If Cordelia didn't actually wakes up from the coma how did everyone besides Angel see her? No one said "weird, we talked to and hugged her and all".
Answer: Everybody including Angel saw her. After helping them and then being left alone to talk to Angel, Cordelia says that the Powers That Be let her come back one more time to help them. After Angel gets a call saying that she died, he realises that it was her spirit that was helping them the entire time.
Answer: They figured they could root out of the real evil that infects the place and do some good with it. Like an undercover cop that joins the mob underworld.