You can find artifacts using the anomaly detector. Usually, the beeping sound is different when an artifact is nearby. Further in the game, you can either buy a better one (with a radar) or just use one from a side-quest (means not returning it to get the reward) :-)
As for zombies and other crap, AIM FOR THE HEAD. 2 bullets are enough if you crouch (reconfig your keys and have 'always crouch' on Ctrl key, so you can use Shift to lower yourself even more).
Have a nice fight ;-) I enjoyed the game, even if it looks more like an add-on - you gotta admit they basically restructured the old maps a bit. Some parts are the same to keep the continuity and game feeling..