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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.

Chandra’s last ability, by contrast, only allows you to cast spells that are red when you cast them, no matter what the card in exile is. If Rowan, Scholar of Sparks (a modal double-faced card) is exiled by this ability, you won’t be able to cast its back face, Will, Scholar of Frost, this way because it would be a blue spell.

You must pay all costs for spells cast via Chandra’s last two abilities. For the middle ability, you must also follow all timing restrictions.

Chandra’s second ability checks the characteristics of the card you exiled to see if it’s red. If the card is red, but the spell that card becomes somehow isn’t red, you may still cast it. For example, Rowan, Scholar of Sparks, the front face of a modal double-faced card, is red. Will, Scholar of Frost, the back face of the same card, is blue. In exile, that card is red, so you may cast either face if you exile it with this ability.

Chandra’s first ability uses the stack and can be responded to, even if no targets were chosen. It isn’t a mana ability.

The emblem’s triggered ability looks for the actual amount of mana spent to cast the spell. If an effect caused you to pay more or less mana for that spell as you cast it, that will be taken into account when determining the value of X. If an effect would counter that spell unless you pay some amount of mana, that mana doesn’t count as mana spent to cast it.