Due to the sheer broadness of the question, I cannot speak for Mehmet, or Singh, but I can speak in regards to Alexander. There are a lot of points either way as to why Alexander was so successful.

The Achaemenid Empire at the time of Alexander was not the same seemingly implacable kingdom that it had once been. It was wracked by internal division: Egypt is able to break away from 404-343BC, the Revolt of the Satraps occurred from 372-362BC, and in 401BC Cyrus the Younger made a failed bid to overthrow his brother Artaxerxes II. During the latter conflict a force of Greek mercenaries famously known as "The Ten Thousand" fought for Cyrus, and following his death made a fighting withdrawal from just north of Babylon all the way to the Black Sea and then to Greece. The fact an army was able to escape Persia in such a manner was a major sign that Persia was weak and was ripe for conquest.

Alexander's father, Philip II, had built Macedon's military from the ground up. He'd changed the way they fought - professionalising his soldiers, having them adopt the sarissa over the shorter and more traditional dory spear. In addition, Philip made his phalanxes twice as deep as was typically done. As a result, Macedonian phalangites were the most formidable in Greece. With this force Philip was able to subjugate all of Greece (bar Sparta) into his League of Corinth. Having done this, Philip readied his army for an invasion of the weakened Persia, before being assassinated in 336 BC, leaving the invasion ready to proceed under Alexander's command.

So in these ways, Alexander did have his work made easier for him. However, when he did invade the Achaemenid Empire, Alexander achieved miraculous victory after miraculous victory - at Granicus, at Issus, at Gaugamela. Even with his excellent army and his experienced staff, one cannot say that he was not at least a competent general. In the immediate centuries after his death he was considered a brilliant general. Although it is likely an apocryphal story, the meeting of Hannibal and Scipio relayed by Appian has both the great generals agree without argument that Alexander was the finest general in history. This shows us what the view of Alexander as a general by writers near to the time was - that he was extraordinary.

So yes, in many ways he did have a lot of factors in his favour - his great army, his experienced generals, the fact that he fought a Persia relatively weaker than it once had been. But even with all these, I would say it's unfair to then discount Alexander's own talent entirely: I think it's fair to say that he was one of the greatest generals of antiquity.

Sources:

Arrian, Anabasis of Alexander. Translated by E. Iliff Robson. London: William Heinemann, Ltd., 1929.

Plutarch, Life of Alexander. Translated by John Dryden. London: Folio Society, 2010.

Bosworth, A.B. Conquest and Empire: The reign of Alexander the Great. Cambridge: University of Cambridge Press, 1988.

Green, Peter. Alexander of Macedon. Harmondsworth: Penguin Books Ltd., 1974.

I can only speak to Mehmet, but the general idea is similar to the points made in the response about Alexander with respect to the Achaemenids by /u/ComradeSomo.

Certainly, conquering Constantinople was no mean feat at any time in the late middle ages (and apparently again in World War I), but the Byzantine Empire in 1453 was terribly far from where it was at its height. It was hardly even an empire anymore.

Let's talk about that first. It was far from being an empire, being confined mostly to the city itself, as well as some largely-undefended territories in the Peloponnese that had been extensively raided by the Ottomans and would fall completely in a matter of time anyway.

To set the stage, the Ottomans in 1453 already had their capital in Europe in Adrianople, and having taken all of Anatolia had surrounded the Byzantines completely. There was no Byzantine navy anymore at all, rendering the strategic position of Constantinople less useful than it otherwise would have been.

Second, let's talk about the protagonists. You know the old joke about how when you write seriously about history, you can at least expect to sell a copy to your mother? Well, I didn't. My mother couldn't get through the proof of my work on the late Byzantines, getting bogged down by the succession of horrible Alexioses and Andronikoses in the 13th and 14th century. She didn't even make it to the siege. The point is, for the 250 years after the fourth crusade, the Byzantines not only squandered any change of recovery that they might have had, the actively harmed their own cause with squabbles, infighting, and succession woes. The last three emperors weren't terrible, but it was too little, way too late.

On the other side was a young and hungry empire. Constantinople by 1453 had been besieged by previous Ottoman sultans, and may have fallen if not for intervening circumstances. Bayezit I (Yilderim) built Anadolu Hisari, the complement to Mehmet's Rumeli Hisari, in anticipation of his siege that commenced in 1395. Bayezit had already consolidated power in Anatolia and conquered the formidable Bulgarians and northern Greece. He got his nickname (which means something like "thunderbolt") for his military prowess on quick marches and devastating strikes.

His siege lasted nearly ten years, and even when western Europe dispatched a crusade to help out their brothers in Christendom, it was roundly walloped at Nicopolis, presaging the defeat of the Varna crusade some decades later. Surely, the city would eventually have to give in, right? There was no one out there bigger or badder than the Ottomans ...except Timur, who laid claim to be the successor of Genghis Khan, and made a pretty good case of it too. Without Bayezit's defeat and capture by Timur, and the resultant Ottoman interregnum, there may have been no Greek Constantinople left for Mehmet at all. Even fifty years before the fall, Constantinople was hanging on by the skin of its teeth.

Third, let's talk about the resources available. Here too, we see an empire under duress and an empire approaching the peak of its power. The manpower was not there for the Greeks - George Sphrantzes reports something like 7000 men in the city in 1453. To put that into perspective, that is about the same number of troops that were just in the Ottomans' elite corps of janissaries. On top of that, the Ottomans had (probably, these are estimates) something like 80,000 total fighting men, from rustics with axes and spears fighting for plunder, to regulars, to cavalry, to the elite janissaries.

Also telling is that cannon, which were relatively new at the time, were being used, and the best cannon founder around was a man named Orban, who was in the service of the Byzantine empire, at least until he realized that there wasn't enough money to pay him. He went over to the sultan. Orban's great guns played havoc with the walls that had kept invaders out for so long, and the Byzantines had nothing to counter them. Again, not to minimize Mehmet's accomplishments, but would he have had as much success had not cannon fundamentally changed the efficacy of city walls viz. siege warfare? Constantinople was ripe for harvest, and the cannon was the mechanical thresher. (Too much?)

I want to reiterate that I am in no way minimizing Mehmet's accomplishment in taking a city that had withstood forcible capture by some of the world's best armies for around a millennium. But if anyone was in the right position to do it, and came to power at the right time to carry it through, it was Mehmet. Even then, it's not like it was a cakewalk, and he had his own issues of faction and power politics to deal with. That a city could hold out for two months with its defenders outnumbered a dozen to one should tell us all we want to know about whether Mehmet had an easy job of it.

But the opportunity was there. Was Mehmet a better general than the others who besieged Constantinople? Was he better than Yilderim, even? Sorry, but the fact that he succeeded where the others didn't is not dispositive. He faced a more favorable situation. But he certainly was extremely capable, driven, and successful. Maybe that's all we need to know.

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