During the damage step, cards that are spell speed 2 or 3 can be activated to use their effect. That means that a player can use quick-play spell, monster's quick effect, normal/continuous/counter traps in the step." Im confused
it actually states the exact opposite;during the damage step you can activate traps and quick spells/mons effects.so yes,if your opponent activates the mirror wall you can chain a twister.It will result in a instant switch from halved to normal attk and then the damage step will end according to its regular outcome.this happens because the mirror wall effect lasts until the trap is on the field.
In my experience twister does not counter the mirror wall effect. If you have two monsters and you attack with the first, this one will be destroyed and afterwards the twister will come into effect and you can freely attack with your second. So my understanding is you CAN activate it in the damage step to destroy a spell or trap but never to counter its effect once it has been activated.