Kiora, the Crashing Wave

Once the first ability resolves, the damage prevention continues to apply even if that permanent changes controllers.

Kiora’s second ability allows you to play an additional land during your main phase. Doing so follows the normal timing rules for playing lands. In particular, you won’t play a land as that ability resolves. The ability will fully resolve (and you’ll draw a card, perhaps a land you’ll play later) first.

If Kiora leaves the battlefield after her second ability is activated but before it resolves, you’ll still be able to play an additional land after the ability resolves.