MTG: Exiling a creature during combat?

Once a creature has been blocked, it stays that way. If the creature that was declared as a blocker is removed before damage, it doesnt stop the creature from being blocked and unless the attacking creature has trample, no damage is dealt. He is definitely permitted to play an instant when he did, he is unable though to play an instant in response to attackers being declared, blockers being declared, or damage being dealt. Between each step (attackers, blockers and damage) there is a chance to play instants or sorceries but attacking blocking and damage happen at the beginning of each of those steps and do not use the stack.