Yes and yes to both.For the first one specifically, you have to attack Seteth with Byleth first. For the second, I just avoided her (using warp, mounts, etc.)
Thanks! I'll give that a go in my future run.For the two green haired weirdos, you need to defeat them with Byleth. I think it's not necessary to defeat both with Byleth (only the first defeated) and it's also possible you only need to engage one of them with Byleth (to get a special dialog before defeating them, which triggers their survival) but to be sure, defeat them with Byleth.
Hilda can't be "spared" BUT is not a requirement to complete the mission, meaning it should be possible to avoid aggroing her, thus not fighting her.
I just wish IS would give us more info on when the difficulty update is coming and what DLC is going to drop.