If I flip at least one black battle icon during the battle, when does Composite Armor do 1 damage to the attacker?
The damage is done after the battle, just after you scrap Composite Armor.
If I didn’t flip a black battle icon during the battle, do I still have to scrap Composite Armor?
It means that any cards that reference being in Plane or Tank mode are active in both of Overlord’s modes. This means cards like Composite Armor can be put on him in either mode. When you flip a Hull Down
in either mode it is active, etc.