I think this can all be explained with him being a sociopath. Its like the scene in schindlers list where the nazi is just randomly walking through the ranks of jews shooting them in the head. Some he points his gun at and doesnt fire.. some he stares down but doesnt fire.. He is the hunter... tracking the actress, closing in, and making the kill.

As for letting the girl live.. he could be doing this for his reputation, as the dairy farmer is not going to ever tell this story out of shame. Also, see above, hes a sociopath. He enjoys 'playing god.' And as for exposing her as a jew later in the movie.. I dont think it was ever made clear that he knew that it was her, in the dairy farmer scene it definitely never shows him getting a good look at her.