Hi, thank you so much for the kind words! I totally missed the notification for these comments.
1. Yes! It's very much at the GM's discretion but I do believe that a meaningful fight should advance an operation somehow and thus reduce its Resistance - maybe it draws out an important enemy, or exposes a plan?
2. Either her or the Dominion for sure! I think the Dominion is more directly destructive while the Canoness is a lot like a Palatine in the lore, with more logistical and leadership duties.