Yeah, a few of the puzzles are really hard if you just don't see it. I think I was trying for half an hour on both those tricky ones before getting it or giving up.
I'm still really early on in Engage, so I can't really comment on it, but between battles I'm just watching the cutscenes and going through the dialogue, not doing any of the optional support conversations or even going back to the base to check the shops etc. so it's quite a fast pace. The story so far feels a bit meh, though - not very epic.
I thought I might try Three Houses after this and just skip/auto as much of the monastery stuff as I could, but if I actually have to do that stuff to recruit people, it's going to get annoying.
So if it gets that far, I wonder if she gets retrialed with a proper statistician to provide comment and different experts, or she is just acquitted?