There was no clear successor when Alexander died due to him dying unexpectedly, so it was only natural that the empire would fragment. Also, though he may have been the greatest of conquerors, he was nothing like his father Philip The Great, whom was a genius when it came to both administration and diplomacy.

Well ... he pretty much did that already, that's why they call what follows the Hellenic Period. Hellenic culture spread through most of the region he conquered and Koine Greek came to be the lingua franca into and throughout most of the Roman period.

But whether he could have forged a unified state ... I don't think so. Alexander's empire was a little too ambitious, a little overstretched. Persia's administrative bureaucracy was very good, but even it had limits - and of course, imposing it on places like Greece, Egypt, Judea etc would prove difficult. The fractionalism of the cultures involved cannot be understated. Had he lived, Alexander probably would have gone down in history as a widely resented tyrant - and when he finally died, a very bloody age would have followed.

Well, the diversity in Qin Shi's empire was not nearly so great. Those groups came from a common cultural sphere, even if there were separate ethnicities and dialects. The gulfs between the cultures within Alexander's empire were much wider. Uniting the traditions of Athens, Jerusalem, and Thebes was something even the Romans struggled with, even after centuries of Hellenization - and that's only a thin westerly slice of Alexander's empire. To this day the area remains the most fractitious nexus of cultures on the planet, bar none.