I'm an elven druid, although I don't specialize solely in any one species of familiar. I have an undead hand, three skeletons, a wolf, a hellhound, and three dragons. My fire dragon leveled up and learned Shape Fire, and my brother saved a beached sea serpent with a Shape Water amulet, and I want to learn Shape Earth. However, I don't know if Shape Earth involves dirt, common rocks, or minerals, or multiple of those. Which ones can I use it on?
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You can use it on all of those.
"Earth" isn't a technical term in GURPS, so it has the English meaning. "Earth" means anything that makes up soil. Soil is composed of rock particles varying in size, from clay and sand up through gravel and small stones. It is often, but not always, mixed with humus—decayed organic matter.
So based on the modern English meaning of Earth, you can use Shape Earth to handle everything you mention. Furthermore, the description of Shape Earth (which is identical in the GURPS 3e and 4e basic rulebooks, and possibly earlier) has been slightly edited in 4e GURPS Magic to include cost multipliers for solid stone and worked stone, without changing the description meaningfully. That implies that "earth" is intended to be understood in the even broader elemental meaning, encompassing everything that is elementally Earth.
Short answer: yes, all of those. Additionally, if you're using 4th edition GURPS Magic, it's all of those plus solid stone, but the costs for it are much, much higher.