Thanks, we also love Neon Genesis Evangelion over here!! We Can (Not) Wait for the final Rebuild movie!
And thanks for the heads up! When opposing a God, you do take damage (and draw a card) as usual. You can also Oppose them until one of you falls. We've updated page 9 to make these rules clearer - and we also added some new rules for escaping a planet when things are going south on Page 10, which was an update we were already playing with and thought this was a good time to include!
Hope you're enjoying your time making Gods regret their ways!!