After using Unown VSTAR's "Star Cipher" attack while Path to the Peak is in play, I then use Spiritomb's "Ticking Terror" attack to change the Defending Pokemon's Weakness to {D}. If my opponent removes Path to the Peak from play, what will that Pokemon's Weakness be?
The Weakness will be {P}. Once Path to the Peak is removed from play Star Cipher's effect will reapply, and the most recent Weakness-changing effect takes precedent.
If I use Unown VSTAR's "Star Cipher" attack while Dunsparce with "Mysterious Nest" Ability is in play, are my opponent's colorless Pokemon's Weakness set to {P} or do they have no Weakness at all?
The Star Cipher attack would switch your opponent's Pokemon's weakness to {P}, but then Dunsparce's Mysterious Nest would change all colorless Pokemon to no weakness.
If I have Galarian Zapdos V with "Fighting Instinct" Ability active and an Earthen Seal Stone attached, and my opponent has 3 Pokemon V in play, can Galarian Zapdos V use Earth Sealing Stone's "Star Gravity" attack for free?
Can I use the VSTAR Powers of Earthen Seal Stone or Forest Seal Stone if they are attached to Pokemon-V that have not evolved into a Pokemon VSTAR yet?
Yes, that is correct. But keep in mind that you still can't use more than one VSTAR Power in a game, even if you evolve the Pokemon V into a Pokemon VSTAR later.
Source:
Silver Tempest FAQ; TPCi Rules Team (2022-11-10)