Forum:Damage = Reptile + Royal oppression

My question, if I have Damage = reptile and the other player has royal oppression active on his side of the field, I take battle damage and activate the effect of D=R can he negate it? Because in the rulings of D=R says it activates during the damage step and the rulings of royal oppression say that you cant activate it during the damage step.

Also, when I special summon a monster with D=R, can they activate bottomless trap hole?