"Root gnome" is awesome.
Why "fungus"? When I think of alchemists, I think of turning lead into gold, as well as flames to heat water solutions of solvents, "spiritualizing" gases, and so on. It is mainly elemental. There is also alot of medical applications, for healing and longevity, but even these seem to use alchemical ingredients. I guess, some of the chemicals come from plants, like scraping dry wine barrels for certain crystals.
Rock gnome = deep gnome = svirfneblin
For svirfneblin, the name is Norwegian, apparently meaning "the black elf mist", a contraction of svart-alf-nifl-inn. Maybe emphasize arctic fog as well as stone. Rock gnome is great for them, and I still want to see a "children of the mist" vibe too.
Actually, I guess D&D already has some tradition about the Svirfneblin, but I would love it, if this is the go-to culture for the "Dwarf / Dark Elf" according to the Norse sources. If so, these gnomes are actually personifications of rock, more like earth elementals. They are human height, not small. They are crazy strong (!), especially in the sense of carrying weight. They are innately magical, and known for making magic items. Oh, and they petrify in direct sunlight! (And Drow thought that they had it bad.) They can create the magical mist during daytime as a sunscreen, to prevent the sun from petrifying them, during the rare times they venture onto the surface during daytime. They also wildshape into animals, including a dragon. I probably associate them most with Intelligence, Wisdom, and Strength, with them being mainly Wizards and Druids. They are also personifications of fate, like elves are, except these are moreso personifications of bad luck and failure, probably are responsible for many cursed magic items, and seem mildly evil, or at least apathetic toward humans.
