Maybe your game key was stolen from another player who was cheating. It happened a lot in the past, but now is quite rare. Of course it does not happens randomly, did you downloaded some program from some not-safe site?

This is usually client lag, based on my 200+ hours experience with Arma2, Dayz Mod and Standalone.

Then it wouldn't be Dayz. Dayz is oriented to be survival game, being a living dead doesn't make sense!

Zeds are already known as "broken" from developers, so don't worry, they will get a rework.
And honestly, the developers has the full choice to make zombies OP: In the mod the first problem were actually op zombies in the city, not players

This is a normal problem since Arma2, not such important to the gameplay

This issue seems to affect all the one-hand weapons. I reported it, here is the link http://feedback.dayzgame.com/view.php?id=11171