If Book of Moon is chained to the activation of Drill Warrior's effect that banishes itself, Drill Warrior is set (face-down) and then it is banished (face-down).
If Book of Moon is chained to the activation of Wind-Up Rabbit's effect that banishes itself, Wind-Up Rabbit is set (face-down) and then it is banished (face-down).
If Book of Moon is chained to the activation of Strike Ninja's effect that banishes itself, Strike Ninja is set (face-down) and it stays on the field face-down, it does not get banished.
If Book of Moon is chained to the activation of Wind-Up Rabbit's effect that banishes itself, Wind-Up Rabbit is set (face-down) and then it is banished (face-down).
If Book of Moon is chained to the activation of Strike Ninja's effect that banishes itself, Strike Ninja is set (face-down) and it stays on the field face-down, it does not get banished.