You must pay the costs for the spell you wish to cast with Chandra's second ability. If that spell has any alternative costs, you may pay those.

If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, those must be paid to cast the spell.

If a spell has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

If you wish to cast the target card, you must cast it while Chandra's second ability is resolving. You can't cast it later in the turn.

Chandra's last ability doesn't change when you may cast those spells. For example, you can't cast a sorcery spell from your hand during combat.

In a Two-Headed Giant game, Chandra's first ability causes the opposing team to lose 6 life.

If you have no cards in hand while Chandra's last ability is resolving, you still draw seven cards and may cast spells from your hand without paying their mana costs this turn.