Round 1. Zillo's not exhausted.

At the end of the round both players ready their cards. Then, mission effects, and after that player effects.

So Vader does his end of the round attack vs Palpatine. 5 damage and pierce 3.

If the defender exhausts zillo, I assume Zillo can't be exhausted until the end of round 2 (when it will be readied again), right?

Thx!

Correct. The Ready step has already passed, so any card exhausted after it will remain exhausted until the next Ready step (unless an ability readies a card before that).

Thanks a1bert!