For my first playthrough I am going with Rhea. I like Catherine more, but I feel her boss is more appropriate story wise.
Second will be Dimitri (as F) again because story.
Third Catherine, because hell with story, I can't wait any longer!
This is thing about church as institution. It's doctrine double as law (which is not inheritently wrong). Going against church is same as going against government.
If you didn't go, she would go against church anyway, but you would be stuck on church route instead of getting option became villain of story with her. Now you can decide follow either branch.
Great! Given I don't have to give Eldegard any kills I might get Catherine (and Shamir) pretty soon.
BTW do we know whether Flame Emperor has its own set of stats?
Well, monastery is certainly biggest own thing, but I don't think it shuffle stuff much. It's just more extensive micromanagement which was always present.