Will a copied spell trigger Prowess?
Collateral damage says:


  As an additional cost to cast Collateral Damage ...


Comprehensive Rule 706.10 says:


  To copy a spell ... means to put a copy of it onto the stack; a copy of a spell isn’t cast. ...


Per 706.10, the copy of Collateral Damage isn't cast, so you don't have to pay the cost again.

Copying a spell does not trigger Prowess. Prowess triggers when you cast a spell, and, as we previously discovered, copied spells are not cast. A ruling on Howl of the Horde reiterates what we have concluded:


  ... Each copy is created on the stack, so it’s not “cast.” Abilities that trigger when a player casts a spell won’t trigger. ...


Some cards actually copy the card (not the spell) and have you cast the copied card. Panoptic Mirror is a good example. Just to be clear, this would trigger Prowess.