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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.

If Sorcerer's Broom leaves the battlefield before its triggered ability resolves, the token will still enter the battlefield as a copy of Sorcerer's Broom, using Sorcerer's Broom's copiable values from when it was last on the battlefield.

The ability of Sorcerer's Broom is a triggered ability, not an activated ability. It doesn't allow you to sacrifice a permanent whenever you want; rather, you need some other way of sacrificing permanents, such as the activated ability of Food tokens.

While resolving the triggered ability of Sorcerer's Broom, you can't pay {3} multiple times to create more than one token. However, if you control more than one Sorcerer's Broom, you can pay {3} for each of their abilities.

The token won't copy counters, Auras, or Equipment on Sorcerer's Broom, nor will it copy other effects that have changed Sorcerer's Broom's power, toughness, types, color, and so on. Normally, this means the token will simply be a Sorcerer's Broom, but if any copy effects have affected that Sorcerer's Broom, they're taken into account.

If you sacrifice Sorcerer's Broom and another permanent at the same time, Sorcerer's Broom's ability triggers for that permanent.

The token will have Sorcerer's Broom's ability. It will also be able to create copies of itself.