Regarding the pieces of rock you have. I can't see a G.I. picking up random shards of rock and carting them back home, they must have had some significance for him to do this IMO.
Below is a couple of photo's of Hitler's fireplace at the Eagles Nest in Berchtesgaden, it was a gift to him from Mussolini and is made of Italian marble, a dark red type with white striations running through it. The borderof the hearth was different in being white stone.
The first one is what the fireplace originally looked like, the second what it's like today after the G.I.'s had a good old hack at it, and the other two are fragments of it that have been auctioned recently.
It may only be a theory; but I think there is a fair chance that at least a couple of these pieces may well be part of that fireplace.