You may activate Ajani’s first ability without choosing any target. If you do, you will gain 2 life. However, if you do choose a target and the target creature is an illegal target by the time the ability tries to resolve, the ability doesn’t resolve. You won’t gain 2 life.

If the target creature is an illegal target by the time Ajani’s second ability tries to resolve, the ability doesn’t resolve. No player will gain life.

Ajani’s last ability affects only creatures you control at the time it resolves. Creatures you begin to control later in the turn won’t gain flying or double strike.