When you activate "Book Of Moon" during the Battle Step to flip your defending monster into face-down Battle Position Defense Position, the attack resolves as normal. No replay occurs because the possible attack targets on your side of the field did not change.
When you activate "Book Of Moon" during the Battle Step to flip an attacking monster into face-down Defense Position, the attack stops. No replay is triggered. The attacking monster cannot change its battle position in Main Phase 2, because it is still considered to have declared an attack. (So it cannot be Flip Summoned in Main Phase 2.
If you are attacking, and you chain "Book Of Moon" to your opponent’s "Mirror Force" to flip one of your monsters face-down, that monster is not destroyed by "Mirror Force".