Wrong, the Klingon aristocracy were shown to be running the show when it came to who was in power, not the warriors. The Klingon council was composed of two dozen of the most powerful families, the great houses.
Not the warriors.
Martok's climb to power by way of being a great warrior was very unusual.
Uhh, no, you're confusing "warrior" with "soldier." The warrior class is the nobility of the Klingon Empire -- the great houses like the House of Duras and the House of Mogh. They're basically like knights in Europe or samurai in Japan -- a class of hereditary nobles who are also the society's military leaders, and whose prestige is largely based in their military identity and power. Martok, by contrast, was a common soldier, one of the working-class grunts that was commanded by the warrior nobility, but who managed to rise from commoner to noble through his military prowess, rather than inheriting a noble title as most in the warrior class do.
No, a stable society remain at a constant level. A declining society is one that loses ground, like your example of the Chinese over time.
The Chinese were not a 'stable' society.
"Were?" China is currently well on its way to becoming the dominant economic and cultural power on Earth, which it's historically been far more often over the past 2000 years than the European West has. Sure, they've had their ups and downs like any society -- Chinese historical theory is based on a cyclical model since they've been through the rise and fall of so many dynasties -- but they've existed as a distinct society and culture for millennia and have been one of the world's dominant powers for most of that time. I'd call that pretty stable, certainly more stable over the long haul than, say, the United States, which is still a juvenile upstart on the historical timescale the Chinese think in.