I believe you are right and it may be a Quartz rock with Gerasol Opal on and inside! Also, the rock appears to have undergone some extreme heat. The other rock, I have no clue on it but it appears to be a composition that is Copper based that flowed into a heavily porous rock formation and hardened.
The quartz specimen is interesting and I've found and have similar material. At first I thought labroradite but that stone, a feldspar, tends to blues.
Here is a picture of what I have:
My speci does not show it very well, yours is outstanding for color, but they appear to be related.
These speci's have the same metallic and iridescent sheen your stone shows. Mine happen to have crystals that are coated with the material. In the larger display the crystals and the rock in the left corner all have the material on them. I gathered those specimens in Australia off an open pit gold mine in Victoria. What I think has occurred is that metallic mineralization, mostly iron but also other metals, have bonded to the quartz similar to the process that is used to make Aura Quartz *a man made item using titanium or gold*. The result is the opal like and iridescent affect you see.
I only found this to occur in a couple of locations however all had very high mineralization and were related to gold bearing deposits in association with high iron and crystallization. A very high temp hydrothermal event.
Its neat stuff. I've tried off and on to find more info on the occurance with little luck but if I find an answer I'll be happy to share it.
As to the banded stone I cant tell if it is metallic or just an interesting banding. Looks like a granite.
I'm wondering if the first specimen is a feldspar with poorly visible cleavage.
At the second photo you can see a crack, gently try to get it to open.
Photograph the flat surface and post, please.
Also try a hardness test with a known quartz, can the quartz scratch it?
Oh, as for quartz. When you see it on quartz its usually a thin layer metal-ish minerals that show iridescence.