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.

If Slagstone Refinery is put into a graveyard from the battlefield or exiled from the battlefield at the same time that one or more other nontoken artifacts controlled by the same player are put into a graveyard from the battlefield and/or exiled from the battlefield, its triggered ability will trigger once for each of them plus once for itself.

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."

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.