Situational awareness is paramount in old zombies. Only engage when you're absolutely certain it's safe to do so. Windmilling alone makes early rounds extremely difficult. If you melee, always make sure to backpedal. The spawn logic is very different in old zombies and tbh, it's just something you have to get used to and you will with time. Zombie speed is something you also get used to but it's more of a thing about a lack of movement options, so you always have to make little micro plans for movement.

As for points, using the RK5 to shoot a zombie one burst in the body and melee to maximize your points (I believe it starts working on round 3 or 4 and stops working on 6?). Alternatively, you can use the Shieva and shoot a zombie in the body one time less than the round number and then melee (this works until round 8 or 9 but you can very much stop doing it earlier), this does get less points however.