Thanks for the advice so far. I spent the first two-three months or so lavishing most of my attention on the Black Eagle students to get them out of their squishy base classes as quickly as possible and given how things have gone since I'm going to work on aggressive courting some of the more brawny guys and gals. Ferdinand and Caspar have been kind of so-so up until now and I don't want to have Byleth and Edelgard carrying the team so heavily in that department since their abilities turn them into EXP sponges. Also, it feels like so far the method that gives you the most professor level experience is picking up those fishing and gardening manuals that are left lying around (and on that note I feel like I have to keep my nose buried in Serenes Forest whenever I'm wandering around the monastery because no one here is capable of keeping track of their personal belongings!)
The most boneheaded thing I've done up to this point is getting careless around the Death Knight and not realizing I had Lindhart parked directly next to him until it was too late. I really shouldn't've Divine Pulsed that fuck-up away because I well and truly deserved it.
Missing items you find belong to the person that was at that location the previous month; not that I expect anyone to remember where everyone was but there's a logic to it. I'm trying to remember if the manual locations are hinted at on the mini-map but I can't remember (there's not a lot anyway). Battalions will give your units some stat boosts to help them survive longer if you find your front line needs work.