Imagine taking any other non-muslim conquerer and saying the shit you and those other faggots said. "Oh, Islam conquered so-and-so because of divisions" - yeah, so fucking what? You don't usually attack a country when it has equal or near-equal power to you, otherwise you get a stalemate like with the Byzantines and Sassanids.
Dude, I'm just showing the reasons as to why the muslims had an easy time conquering those places, I never mentioned wether I personally think that using your enemy's disadventages was weird or cowardly, because it isn't, it's a valid strategy that works.
Small note regarding the stalemate, the Persians almost won their last war against the Romans managing to occupy all their provinces outside of Europe but had to sign a white peace after the Roman Emperor Heraclious suddenly appeared in Anatolia with a massive army of mercenaries and inmediatly went into the Persian heartland.
What, you actually think Alexander fought the Achaemenid empire at its greatest strength? The country was divided, because half of the satraps didn't accept Darius III who was a usurper.
Of course those weren't the Achamenids at their peak, I know that, but the Empire wasn't in economic and military ruin like the Romans or Sassanids were, and while a lot of the satraps were probably planning on overtrhowing Darius they still fought Alexander, with some exceptions of course, like the Satrap of Egypt who just gave away his Satrapy when Alexander showed up; however, Darius while being disliked by his subordinates he was still the King of kings, ruler of the largest Empire of his time and he still managed to assemble armies far larger than that of Alexander, but he, along with his generals, still lost.
Westerners should be glad there existed a New World, otherwise they'd be stuck on Asia's peninsula.
Eh, that's debatable, the ones who beneffited the most of the discovery of the Americas were the Spanish with all those gold and silver mines along with most of the Caribean being sugar plntations, the French had Haiti wich produced lots of sugar while Lousiana and Quebec were just there, the British had the Thirteen Colonies wich were autonomous and the Portuguese had Brazil also producing sugar. But the British, French and Portuguese were far more interested in getting into India than the Americas, since Spain had already gotten the large gold and silver mines.
As a clarification, dumb luck is something that affected all sort of events across human History, like when the 2 mongol invasions of Japan were struck by huracaines sinking a good chunk of their fleet, or when Christians in the first crusade suddenly discovered a holy relic that restored their morale, or when the tribe of the Cimbri destroyed an entire roman army and instead of going into Italy they went to Iberia wich allowed the romans to prepare for the next battle.
To summarize, you might be the luckiest man in the world but all that luck is meaningless if you don't know how to properly take avdentage of it.