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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

Any choices made when the spell resolves won't have been made yet when it's copied. Any such choices will be made separately when the copy resolves.

You can't choose to pay any alternative or additional costs for the copies. However, effects based on any alternative or additional costs that were paid for the original spell are copied as though those same costs were paid for the copy.

Feather, Radiant Arbiter's ability triggers whenever you cast a noncreature spell that targets only Feather and no other object or player.

If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copies will have the same mode. You can't choose different modes.

The token that a resolving copy of a permanent spell becomes isn't "created" and won't interact with abilities that care about tokens being created, such as that of Case of the Pilfered Proof.

If a permanent spell is copied, the copies are put onto the battlefield as a token as the spell resolves rather than putting the copy of the spell onto the battlefield. The rules that apply to a permanent spell becoming a permanent apply to a copy of a spell becoming a token.

The copies created by Feather, Radiant Arbiter's last ability are created on the stack, so they're not cast. Abilities that trigger when a player casts a spell (like Feather's own ability) won't trigger.

If the spell that's copied has an X whose value was determined as it was cast, the copies have the same value of X.

You control all the copies, and you choose the order the copies are put on the stack. The original spell will be on the stack beneath those copies and will resolve last.

If you cast a noncreature spell that has multiple targets, but it's targeting Feather, Radiant Arbiter with all of them, Feather's last ability will trigger. In that case, each of those copies will also only target one of the chosen creatures.