Chandra, Dressed to Kill

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.

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

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.