Re: When do you activate 'Draw their Fire' (or can you read that crit first) ?
When a friendly ship at Range 1 is hit by an attack, you may...
That's the trigger condition for Draw Their Fire. A ship is hit by an attack after you've done all the canceling, and have leftover hits. So that's when you'd have to decide to activate Draw Their Fire or not. No waiting until the damage starts resolving.
And, to put it even more explicitly:
You have to decide whether or not to use Draw Their Fire before you start dealing out damage cards, so you won't be able to see the damage card first.