Addressing is every volcano a mountain:
Nope. Some are actually depressions called calderas, when they have erupted and the resulting emptying of the magma chamber caused the roof to collapse, or if they erupted only once, leaving behind a maar. Examples: Yellowstone, or Phlegrean fields are calderas, volcanic Eifel has "Maare" (German plural of Maar).
These are most likely manganese dendrites. It is not a fossil, and not organic. These usually form in cracks in rocks, and most likely this slab was broken along an existing crack.
You can read more about it now: https://www.mindat.org/min-26645.html
One comment: this is not basalt. Basalt is black. Most likely some form of limestone.
They are quite pretty, but they are not fossils. They remind me of the patterns that frost sometimes makes on window panes. A similar process is at work here, though with mineral bearing water infiltration rather than frost being the cause. The water infiltration deposits crystals in the rock.
Yes, there would have been seas of lava glowing in the night, but not as large as the lunar mare. The lunar mare were caused by asteroids punching through the then thin lunar crust and releasing a flood of magma from below, as well as producing some magma of their own from the heat of impact. There is no evidence of anything of that nature causing the ...