Thought I'd chime in for a couple of things (mostly conceptual, since it is what drew me to this thread in the first place, and I've reached my patience threshold for coding and debugging in the past week, so I'm not too keen on learning to mod this game right now^^)
For the UA name, I'd have two suggestions, the first in line with what Arachnofiend suggested (namely "Shepherds" or "Shepherds of Ylisse"), since it thematically fits with Emmeryns Ylisse. To make it more thematically linked to the Shepherds, it could encourage active city-state play by increasing quest rewards (especially barbarian quests, since the Shepherds role was kinda to run around smacking bandits), or the range at which killing barbarians near city-states give influence. Though I'm not sure how easily it could be implemented (especially that last part).
If you'd like to keep the more passive approach, I'd suggest "Renewal". Just because Chapter 10 (and what happened just before) was the most bittersweet Fire Emblem Chapter I've ever played, depressing but invigorating at the same time. "Renewal" summarizes everything Emmeryn did since she became exalt. Furthermore, this name would fit the more passive angle of the UA, in a kind of "Emmeryns reputation preceding her". As for the actual implementation, instead of reputation per turn, you could try for increased resting point, since the reputation increase only happens below friendly, and I assume people would play Ylisse with Consulates and even Papal Primacy (would make sense with CS UA and religious UB), but ironically, the UA turns out to be useless if you pick those. Though it would go against you reluctance to give them a "free friends" ability, and would be really powerful in conjunction with the second part ("Wanna attack me? Well, enjoy losing 500g worth of influence per ally!").
As for the UB, I really think a religious UB is most fitting, considering Ylisses distinguishing point as a nation is their devotion to Naga. I do agree that a flat bonus seems a bit "meh" for a custom civ, no matter how powerful (1 happy on a cheap building you want everywhere if you go for religion, or 2 if you get the synergistic belief, seems quite strong tbh). If you want something more fancy, what about bonus food/growth when at peace (akin to swords to plowshares). It would be thematically very fitting with Emmeryns rule of the Halidom and general aversion to war the country has. Though again, would sound easy on paper, but I am not sure about implementation, especially for the %growth part (afaik there is no existing local %growth building by itself, so idk if it is actually feasible).
Well, my 2 cents about the missing concepts, I hope it can help. At any rate, keep it up, in the name of all the Fire Emblem fans out here!
EDIT: Oh, forgot about Galeforce for Pegasi. Never forget Galeforce! Free blitz for the Pegasi, so they actually have something to transfer when upgrading. Though it might end up kinda OP (which is in line with the actual in-game ability I guess, so still thematically fitting)