Point the first: the Law.
a) Who or what enforces it?
b) Was it created by extant races, or is it an automated holdover from something earlier?
c) Is there a practical purpose to it beyond 'preventing interstellar warfare'?
1. Is it a moral issue (unlikely, given the sort of things the League does allow) or is there maybe something more in lives, in the concept of sentience, that the League finds valuable?
d) Was there some dramatic interstellar war in ages past that first prompted the creation of the Law?
e) Does transcending give a being a clean slate when it comes to the Law? Could a dangerous non-sentient transcend, have a change of heart, and then wander around through space?
f) And, of course, what are the League's provisions for the aforementioned changes of heart in general?
Point the second: the members and their game.
a) What kind of power continuum exists among the members? Specifically:
1. Las Fuentes are young, only 6,500 years or so into the Higher Being schtick. So they can't be that powerful in the grand scheme of things. However, they're players in the game.
2. The Pollisand seems fairly powerful as Leaguers go. He also strongly implies that he's the Devil, or at least the source of that particular figure in human thought, which makes him a very Western 'hero'--which would imply that he's Festina's patron, but see below. How powerful is he? If he's using the same general gameboard as Las Fuentes, he can't be that powerful.
3. Let's call the aforementioned players on the 'same general gameboard' the second-continuum races.
i. First-continuum races include humans, Divians, Cashlings, Fasskisters, Mandasars, etc. Barely sentient types.
ii. Second-continuum races include the Balrog, the Lucifer, Las Fuentes, the Pollisand, possibly the Peacocks--I'm not sure what else.
iii. Postulate that there are also third-continuum races, who might even be the ones in charge of the League. How much do the second-continuum races know about them? Is the game perhaps an attempt to figure out how second-continuum races become third-continuum races? Are third-continuum races true gods? Can they leave the confines of the universe?
b) We can probably assume that all the aliens seen by Youn Suu's mother in the temple are players in the game. Youn Suu's version of the vision is more detailed and gives more clues about who's been chosen by each. That means:
1. "...the Buddha in the fountain, entirely coated with glowing red moss..." The Balrog, whose pawn is Youn Suu (he likes Kaisho, too). Damn, I need to find my copy of Hunted. In any case, he claims the Buddha statue--the Eastern Hero ideal.
2. "The purple jelly had climbed up a chiseled image of the Holy Madman of Pegu..." Las Fuentes, whose pawn is Tut.
3. "...the noble features of King Thagya Min were obscured by smears of what looked like crawling black sand..." I believe this is the Lucifer prior to its recent mutation, if I'm remembering Trapped right. Next on the agenda: seeing if King Thagya Min is an actual figure of legends and, if so, what he's like. Perhaps a classic leader-type?
4. "A granite rendering of Buddha's lovable but dim-witted disciple Ananda was surrounded by a whirling cloud of dust..." I have no idea what this one is. Guess I might have to even reread Commitment Hour just to see if a second-continuum race shows up.
5. "Hui-Neng, the Sixth Chinese Patriarch and founder of Zen, had scarlet lava dripping down the right half of his body, while the left had turned to glass." My guess is that the lava half represents the Pollisand and the glass half represents his pawn. Which contradicts the later assertion that the second-continuum races draw their pawns from the Explorer Corps, although Oar is technically an Explorer now. Still, the Pollisand obviously likes Oar. I'd have thought he'd be the one in charge of the Western Hero archetype, being the Devil and all, but this suggests far too strongly that he's chosen Oar. So what is she? The Bold Child? The Tale of Growing Up?
6. Also mentioned are flames (no idea who that is), blue-leafed vines (again, no clue), and cottage-cheese goo, which is probably the new Lucifer.
i. This suggests that second-continuum races who were originally the same species but then diverged can wind up different enough to take separate pawns.
ii. If so, will the newly-transcended Shaddill/Las Fuentes (as well as the Greenstriders and Unity humans with them) from the end of Radiant pick a pawn themselves? The redeemed villain, perhaps? Except that I'd be more inclined to say that the Peacocks would choose that, if they take part in the game.
c) Who is Festina's patron? My original guess would have been the Pollisand, for reasons outlined above, but he's apparently taken a shine to Oar.