Does Blue Kai'Sa's conquer trigger resolve before or after gaining the conquer point, and does this affect what spell costs you can cast with her ability?

Ruling: Conquer points are gained when you conquer as normal, so you get your point from conquering before Kai'Sa's conquer trigger resolves. If you're at 3 points and conquer with her, you'll be at 4 points when her ability resolves, allowing you to cast 3-cost and lower spells.

Nuances:

• The confusion arose from a mistranslation of a Chinese judge FAQ about "win a combat" triggers (like Draven, Audacious), which resolve before conquer points are gained
• "Win a combat" triggers are different from conquer triggers and follow different timing rules