Welcome to the forum; couple of quick questions.
Did this come from the Sturgess collection? i.e. did you buy it form Simpson, LTD or someone else? I am guessing, but Simpson has always gone overseas and bought items, so it could have been any bulk buy they came across I would guess.
The K - don't really know, its kinda hard to see in the picture but I have not seen one like that.
I am pretty sure that walnut and beech were used, especially in 1918 - I think walnut was hard to get by then.
There is no such thing as a run of the mill luger
