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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.

Auras attached to the exiled permanent will be put into their owners' graveyards. Equipment attached to an exiled creature will become unattached and remain on the battlefield. Any counters on the exiled permanent will cease to exist.

If Static Net leaves the battlefield before its first ability resolves, the target permanent won't be exiled.

If a token is exiled, it ceases to exist. It won't be returned to the battlefield.

In a multiplayer game, if Static Net's owner leaves the game, the exiled card will return to the battlefield. Because the one-shot effect that returns the card isn't an ability that goes on the stack, it won't cease to exist along with the leaving player's spells and abilities on the stack.

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."

Static Net's first ability creates two one-shot effects: one that exiles the permanent when the ability resolves, and another that returns the exiled card to the battlefield immediately after Static Net leaves the battlefield.

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.