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Sarinth Greatwurm's second ability triggers whenever a land enters the battlefield under any player's control, not just under your control.
Powerstone tokens are a kind of predefined token. Each one has the artifact subtype "Powerstone" and the ability ": Add . This mana can't be spent to cast a nonartifact spell."
Although all the cards in The Brothers' War that create Powerstone tokens create a tapped Powerstone token, entering the battlefield tapped isn't part of the token's definition. Notably, if you create a token that is a copy of a Powerstone token, the token copy won't enter the battlefield tapped.
You can use the added by a Powerstone token on anything that isn't a nonartifact spell. This includes paying costs to activate abilities of both artifact and nonartifact permanents, paying ward costs, and so on.
