Hal has an ambivalent relationship towards Eve. On the one hand he likes to protect her on the other hand he finds this little baby pretty annoying. He has never taken care of a baby before, so he doesn't have the social skills to do so. He feels helpless when Eve cries and doesn't know what to do. However the more time they spend together the closer they get. Hal also likes the idea, that Eve is the war child. He hopes that she will kill all vampires, even if that includes him as well.
In the Alternative World until 2037 Hal is the most evil vampire after Mr. Snow. Eve is scared of him and calls him a monster. That is why she sends him to Annie's house, after she travelled back in time. She hopes that he will kill her as a baby, but in this world Hal is different. Eve soon realises that and looks for someone else who would kill her.