The strongest hero.

So why didn't the all-powerful Overlord win this war, and moreover, allowed himself to be cornered, especially since he was not fighting against gods - dragons? Did he simply not want to?

How can he win the war if all his warriors have perished? It wasn't him who allowed himself to be cornered; it was his miserable servants who failed to hold the line and let the enemies into Shio.

The War of the 4th Eclipse cannot be considered a victory, except for the capture of the capital by demons; nothing else is known. It is quite possible that after that, they were driven back by the combined forces of the duchies of the Empire, but I repeat, there is no information about the further actions of the demons. And the main goal of Kha-Belekh in that war was to eliminate absolutely all representatives of the Falcon dynasty, which he failed to do, and based on this alone, one can say that the demons failed in that war.

No, this war was indeed won because the enemy kingdom ceased to exist, and a new one was formed only after the eclipse. But the goal - to destroy the Falcons - was not achieved. However, from the point of view of "interstate relations," the demons won and could have imposed some agreement that was beneficial to them and forced them to pay reparations, if they could have stayed. Although, what reparations could there be; they would have burned everything down.

The purpose of storming Shio may be one thing: the complete destruction of the demons, which is only possible if all the countries and peoples of Ashan unite their efforts. So, here, the claims are against all of Ashan, and not just the Empire, since storming Shio with the forces of only one Empire would definitely be madness, which was proven by Alex Griffin.

The Empire was not alone there. Three major kingdoms opposed the demons, so they can be credited to Ashan. And this was clearly not madness, since three kings decided so, two of whom lived quite a long time and gained experience and wisdom.

Again, why didn't he have enough strength and power to defeat the Gray Alliance?

Again, there were no military forces, but he did kill Alex. One is not a warrior in the field. And the elves and mages retreated. But since he himself no longer had any armies, and the Gray Alliance ceased to exist, it's a draw.

You contradict yourself. In one case, the demons were cornered, and no one won, but in the other, it turns out that the demons, who were supposedly cornered, defeated the Gray Alliance and put Alaron and Cyrus to flight.

I expressed myself incorrectly; I apologize. The alliance fell apart; that would be a more accurate statement. And therefore, neither side could claim victory.

Eternal, not eternal, but there is nothing eternal in Ashan, and even the one who created it can destroy it. So, yes, Kha-Belekh is a very strong and mighty demon, undoubtedly long-lived and not aging, but still not eternal in the absolute sense of the word.

I already wrote about this; he lives as long as the world lives. For Ashan, he can be considered eternal. If Ashan disappears, Kha-Belekh will disappear as well.

In fact, it is known that he, being the first mage, spread the doctrine that everyone can achieve the power of the Elemental Dragons, and he succeeded. He achieved the consciousness of Ashan (which, apparently, even the Elemental Dragons could not do) by his own efforts, and no one helped him in this.

It was not he who achieved the consciousness of Ashan; it was Ashan that revealed itself to him. This is where Ashan helped him. Ashan arranged the world so that no one could achieve the power of the Primordials until the Primordials themselves wished it.

One of the 7 (8) original Demon Lords is just an ordinary archdemon?
in status, he is equal to an Elemental Dragon.
And Sar-Elam was indeed an ordinary mortal who, as Ment noted, surpassed the Overlord in progress and power.

Here lies the contradiction between the fifth and sixth games. In the fifth game, an archdemon is just an ordinary devil. But in the sixth game, an archdemon is a demon lord. In this case, Kha-Belekh was an archdemon-lord, just like the other lords.
In terms of status, no one is equal to the Elemental Dragons except the Elemental Dragons themselves. Demon Lords are not Primordials; they are just the ordinary leaders of Shio. If the lords were dragons, Ashan would not exist.
Sar-Elam, although a simple mortal, is (I'm tired of repeating) endowed with the power of the Dragons. He could not have achieved this on his own; Ashan was involved here.