You can use the {C} 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.

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.

Powerstone tokens are a kind of predefined token. Each one has the artifact subtype "Powerstone" and the ability "{T}: Add {C}. This mana can't be spent to cast a nonartifact spell."

Sarinth Greatwurm's second ability triggers whenever a land enters the battlefield under any player's control, not just under your control.