What does the theocracy get out of it, besides ideological superiority?

They do think having a more competent trading partner and buffer state would be nice.  But a lot of it really is ideological, they are a country of religious fanatics after all.

(That makes them harder to deal with).

Is the ideology on a local level, or mostly confined to the leaders?

Its pretty widespread.  The populous is arguably worse actually.  They are a bit less committed, but also less pragmatic about making compromises.

(Well, that'll complicate things if she ever needs to conquer them. Which isn't a goal, but Takeko likes having her options laid out.)

What are the details of the theology, as far as the common man holds to?

Six hundred years ago the Six Great Gods came to save humanity.  They saved us from extinction, protecting us from monsters, teaching us magic, and granting us Godly Equipment. But they disappeared one by one except Surshana who was defeated by the eight greed kings.  Also all non-human are threats to humanity, but different species run the gambit from merely being competition for resources (e.g. dwarves) to evil for evils sake (demons, undead ect).

What's the deal with undead?

They all hate life want to kill everything, especially humans. They mostly spawn randomly from dead bodies that aren't given proper burials, but can be created by magic.

Apparent intelligence? Power levels? Immunities, weaknesses?

All variable, intelligence and power level are loosely correlated with each other and rarity. Typically weak to fire and holy magic, and immune to all mental effects, poison, paralysis, stunning, sleep effects, and death effects.  He then gives an extensive list of undead that mostly matches undead from the low to mid tiers of YGGDRASIL monsters, with the discrepancies all being about creatures he is not particularly familiar with. All of the mid tier ones are considered to be major bosses who likely control their own dungeon or maybe flat out myths.

"What constitutes a proper burial, here?"

Its actually not a binary thing, and generally speaking its about showing proper respect for the dead rather than specific actions per se.  That said the main things are putting the body underground or in a purpose build mausoleum, having a grave marker, and having some sort eulogy or prayer for the dead said at the funeral.  Having people visit the grave afterwards also helps. 

That should be doable. What happens if you destroy the body?

(She's going to assume that applies to her own people as well, and makes a note to put 'consistent funerary rites' as a high priority for the dead.)

Ghosts/wraiths.  Unless you cremate them and treat ashes like a body.  From what we know about demi-human society we think cannibalism also prevents undead but lets not go there.

Indeed not.

(So she'll need to be careful with her more destructive spells, at least enough so to gather people's ashes after she zaps them.)

So, in order:

Demons? Elaborate.

What's going on with the declaring attacks?

Who were the greed kings, and are they still relevant today?

Demons are powerful magical creatures that enjoy inflicting pain an suffering.  They are believed to come from another world, imaginatively called the demon world, but thats a bit speculative because you can't trust anything they say.  

Well besides actual spells warriors can learn martial arts that let use special abilities.  Its really not his area, but some well known ones are x fold slash(es) of light, and fortress which negates attacks below a certain level.

The Eight Greed Kings appeared 500 years ago an conquered most of the world before having a falling out and destroying each other.  All dead now, though their floating castle is still intactish.  The platinum dragon lord lives there now.

(She might want to look into learning some of that, later.)

Who is the platinum dragon lord?

The most powerful of the remaining dragons.  He's also one of the few people who can still use wild magic.  After a brief pause he decides that its worth volunteering information on wild magic unasked. Wild magic used to be popular before tier magic was introduced.  It was potentially more powerful than tier magic, or a least the tiers anyone normal can reach.  However it requires sacrifices, and can only be used by true dragon lords, their descendants, or people with rare Talents.

(So people to watch out for).

Any major players with it?

The Argland Council State has most of the remaining dragon lords, including the Platinum Dragon Lord.  All of the other living ones are inactive and/or hiding beyond the areas the Theocracy has contact with.  Which to be fair only covers a quarter of the planet maybe less.  

And a modern dragon lord would have a hard time soloing a Dominion Authority?

Probably, but its hard to say.  Its known the wild magic itself has declined in power and that the strongest dragon lords were wiped out by the eight greed kings, but its  not like the empire has convinced the two to come fight in their arena.

(So she should avoid convincing every single person on the continent to team up against her at once, it sounds like, but - there's very few well-known direct attacks she'll need to be fully paranoid about.)

(Which means indirect attacks - subversion, information warfare, assassination - are her relative weak spot.)

"Details on the military strength of the other polities?"

Council State ~= Theocracy >Elf Country if the king doesn't fight > Empire > Beastman Country > Dragon Kingdom > Holy Roble Kingdom > the various small tribes of non-humans inside the human lands> Re-Estize Kingdom 

There are a lot of powerful non-humans in the areas they have less information on, and if all of the local ones united it would be a big problem. But this area remains the human lands because only the Elfs, Beastmen and Dwarves have proper countries rather than tribes.  The dragon kingdom is mostly human they're called that because the royal family has a single dragon in their ancestors.

"Who's allies or enemies with who?"