In order to answer this question, we need to start with Alexander's father, Philip of Macedon. It was he who created an unified kingdom and a standing army. This is not to say that Alexander was not a great general, but it is to point out that Alexander would not have been the man he was apart from the work of Philip. Here are few important military innovations that Philip and Alexander used:
- New phalanx formation, which was deeper. This was created by Epaminondas, the great Theban general. It is interesting to note that Philip grew up in Thebes.
- Longer spear--two handed pike (sarissa) gave the Macedonian an advantage both offensively and defensively.
- Coordination of various type of troops--infantry, archers, light and heavy cavalry, etc.
- Most importantly, there was a professional army.
These points and Alexander's brilliant tactical mind enabled Alexander to conquer the Persians and go as far as India.
As for his legacy, it really depends on whom you ask. If you ask the Romans, they admired him. Caesar wept when he was a young man, because he did not conquer as much as Alexander. If you ask the people whom Alexander conquered, they hated and feared him. Even in Afganhistan today, there are folktale of Alexander, the demon (not the great)!
Speaking generally, Alexander's legacy is one of a great general--probably the greatest general. Even Livy the Roman historian admits this.
Finally, as for why his empire was short-lived, there are two main reasons. First, his successors (Diadochi) did not like each other, and so they not only carved out his empire, but they fought each other. Hence, a unified kingdom was an impossibility from the start. Second, his empire was too vast to be ruled from a single location.