So, the target gets the face-up damage card placed here “when you would suffer 1 [crit icon].”

How does this interact with shields? If my Falcon (with 2 shields remaining) has been “shown the dark side,” and takes a critical hit, then it “would suffer 1 [crit icon],” and normally just lose a shield, right? But in this case, wouldn’t the damage card on ISYTDS be given to it instead?

Yes, that's right. ISYTDS can still trigger when you have shields up, and instead of taking the critical damage (which would normally mean losing a shield) you are dealt the card.

15 hours ago, Cpt ObVus said:

So, the target gets the face-up damage card placed here “when you would suffer 1 [crit icon].”

How does this interact with shields? If my Falcon (with 2 shields remaining) has been “shown the dark side,” and takes a critical hit, then it “would suffer 1 [crit icon],” and normally just lose a shield, right? But in this case, wouldn’t the damage card on ISYTDS be given to it instead?

Generally you pick Panicked Pilot...