You choose whether or not to target a creature as you activate the first ability. If you chose a target creature, you choose whether to exile Kaya or that creature as the ability resolves. If you chose a creature and that creature is no longer a legal target as the ability tries to resolve, the ability doesn't resolve and none of its effects happen. You won't exile Kaya or lose 2 life.

If you didn't choose a target creature for the first ability, and Kaya isn't on the battlefield as the ability resolves, you'll just lose 2 life. No card will be exiled or returned to the battlefield.

As the last ability resolves, each opponent will choose a card to discard and set it aside. Then all those cards are revealed and discarded simultaneously.