But there is one thing I think they shouldn't have glossed over [...]
Yeah, that, to me, is the single most horrifying thing in this whole story, even beyond Bruce threatening Althea with the AO. For beating up Clark, Bruce thinks she needs forgiveness, but not for burying J'onn in flame? Beyond anything else I've ever seen with them, this story is a testament to me of the true depth of the J'onn-Diana friendship, that he's just like "I get it. It's cool," after that.
When Batman says "flatten geneva", what does he mean?
From his perspective, Diana's trying to get the League to stay out of the fight and let the dragon do whatever the hell she pleases, just to protect their own lives on the say-so of empty words; it's not clear to me whether he thinks Diana also intends to stay out of the fight, or whether he just assumes that Diana can't win alone against a League-level threat, but either way, his understanding of the situation begins and ends with "if the League does not stop the dragon, the dragon will pillage and destroy." (Which is true, as far as it goes.) The prophecy is totally irrelevant to him; all he sees is "bad guy will do damage if not stopped, Diana is trying to stop the one thing that can stop the bad guy."
How does the lasso work, exactly?
Heh. This is a worse question than asking about Donna. No one knows. No two authors agree. Gail is right now off on some what-the-hell tangent that will be as close as we've gotten to an actual definition of the thing, which, like Byrne's completely opposite as-close-as-we've-gotten-to-a-real-definition take, will be promptly ignored by the next author out. But the general rule is that simply brushing against it, as she does when it's clipped to her hip, is not sufficient to provoke the magic - you need to either have been holding on to it continuously for enough time for it to kick in, or be completely encircled by it or have a couple of loops around a limb in full contact. Also, it works more, better and faster when Diana provokes it to do so consciously, which would imply a certain freedom on her part to consciously suppress its milder effects on herself as well.