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1. What do these Soul Stones look like? Gemstones? Rocks? Palantirs? Volcanic rock?
I would suggest rather beautiful forms of metamorphic rock. Marble, mylonite, zeloite, blueschist, eclogite. All as polished balls of about the size of a head.
2. What if the stones have been shaped into something else? a weapon? or they are part of a weapon?
The stakes are higher if the Soul Stone is part of a weapon that is used by an enemy that must be defeated.
Well, but that would take away the option for the players to loot enemy magical weapons for themselves.
3. What powers to they have? Do the stones cause magical effects in the environment they occupy?
My suggestion: Each vampire soul can of course cast the magic they could cause while corporeal. However, for it to affect anything, the stone must touch it. Therefore, the stones are stored in floating storage, where they do not touch anything.
4. Have the Vampire Lords trapped inside it corrupted the stones magic or corrupted the ones who found it?
5. Maybe the Vampire Lord still can influence followers from inside?
See 3. If someone found such a thing, they might be under the vampire soul's spell. Literally.
6. Where were the Soul Stones hidden? underwater? in plain sight? under a mountain? in a dark tower guarded by spirit knights?
Special, hidden, very remote installations built or repurposed by the Order to keep the stones floating. One is a tower, one is a deep cavern, another is an old palace of a long defeated demon prince, one is a floating isle in the sky, and one is an enchanted jungle.
7. Why were the Soul stones not destroyed? How can they be destroyed?
Destroying them would mean to liberate the souls therein. Don't.
8. How is the dark ritual to free the vampire lord inside completed?
Destroy the stone. However, it is magically protected against mundane forms of destruction. Each stone has a different way how it has to be destroyed in order to cirumvent that protection: Throw it into a specific volcano, but not one named Mount Doom. Crush it under a Hammer of a Titan. Shatter it with a high-level sorceror spell. Let a dragon chew it to dust. Let a certain, rare type of demon swallow it.