You must follow the normal timing permissions and restrictions for the exiled cards for Chandra's first and last abilities. If one is a land, you can't play it unless you have land plays available.

Because it's a loyalty ability, Chandra's last ability isn't a mana ability. It can be activated only any time you could cast a sorcery. It uses the stack and can be responded to.

If you have no cards in hand, you still exile three cards while resolving Chandra's first ability and you may play them this turn.

You'll still pay all costs for a spell cast this way, including additional costs. You may also pay alternative costs if any are available.

If you don't play the exiled cards, they remain exiled.