I haven't read that source material, but I am familiar with the Exalted counterparts of those three, which are easy to pick out just from the names and your brief descriptions. ("Release the Kukla!")
It makes some sense for Chaos to be the one to come up with a creative solution to a novel problem (and for Evil to be the one who wrecked ****).
So... Law never uses its influence to manage things more effectively by improving efficiency, reducing costly internal conflict, etc.? Followers of the Lawful god in different organizations don't, say, collude with each other for mutual benefit, subtly shifting competing factions towards peaceful coexistence, then alliance, then eventually formal union, until a single society of elites dominates the entire world behind the scenes, while official rulers serve as mere figureheads who can take the fall whenever things go south? Instead, they all just suck at their jobs? Chaos will always triumph, because Law is dumb?
If you say so. Seems kind boring to me.
Some have opined that D&D's Monks are out of place in a game with character archetypes generally fairly rooted in medieval European folklore, but I dunno, I think that Friar Tuck is pretty good with a quarterstaff in at least some of his depictions? Regardless, being a member of a religious order isn't the same thing as being a member of a clergy, although one can of course be both (an okay if not great multiclass); so it makes sense for Monks to be their own different thing from Clerics in a game that has more than one religious class regardless.
Which technically makes Paladins a special type of Monk, I think? Huh.
So Warlocks and their patrons are just weird Clerics and deities? If anything, I'd go in the opposite direction, with the Warlock receiving a one-time infusion of power in exchange for a one-time service. The service is probably something significant and difficult, with a penalty (usually forfeiture of the Warlock's soul) if the service is not completed by deadline.
I'm not sure how you meant it, but this sort of usage of "actually" seems like an indicator of mild surprise to me; in this case, the surprise being that the philosophies presented can be described so well so succinctly. But that's a little weird, since those philosophies seem so clearly to each be built around a single simple core concept which isn't hard to identify or give a word for. Maybe it's me.
I've gathered that Dragonlance's "Good" and "Evil" factions each have an ideology or way of life that they want to bring everyone over to, whereas "Neutral" wants individuals to be free to choose their own path. So it's basically set up as Lawful Good vs. Lawful Evil vs. Chaotic Neutral, not that it's reflected in the deities' alignments, nor that they acknowledge that e.g. a Chaotic Good character may well be more sympathetic to "Team Neutral" than to "Team Good".
Well, that all depends. 3E made Good and Evil essentially just kindness and cruelty, with Law covering morality in a relative sense. AD&D was different, but there it was pretty clear that Lawful characters want some sort of Authority to enforce some sort of Order, whereas Chaotic characters aren't really willing to trust anyone with the power to do that, or at least not enough to cooperate unquestioningly. Conflict between the two is thus expected and natural.
The exclamation point is part of the title.
Fooour sharks in the water....
But really, I don't think that any version of D&D has ever given a description of alignment that doesn't require "boiling the stupid off" to even use consistently, and there are various different ways to modify things to be less pants-on-head. One can discuss the merits of different approaches to that, but it tends to be a bit futile to talk application of some categorization schema before said schema is even sorted out.