According to the SN shown, your gun is not an ejector model. It will have a one piece extractor, which will only lift the shell far enough for you to pull it out by hand.
The "counter sunk screw" you speak of on the side of the stock head is an oft' seen repair to hold a split stock head together. Not necessary for a new stock.
Here's some pics of an extractor
Here's a damaged stock head that was held together with a wood screw. Is this what you were talking about with the "counter sunk screw"?
