Alexanders protagonist...if even that, was Darius. Also he wasn't inspired by vengeance, but with lust and at the beginning; national prejudice.
On a second note, I don't believe Caesar was ever inspired by Alexander. They came from two different cultures with different beliefs, views, etc. Napoleon on the other hand was a student of military history I believe. I don't know who his heroes were, but Alexander could have been on of them.
Pay no attention to darmaster, he's an idiot. Panos, despite his obvious bias, is totally right. Roman culture, military, laws, literally everything that made them a civilization, had greek origins, initially from the Etruscans and Magna Grecia, later from the conquest of Sicily, the greek mainland and greek Anatolia, not to mention the dozens of greek colonies spread around the Meditterranean . Of course they were not identical, and greek culture itself was an amalgamation of tons of different cultures, from egyptian to persian to babylonian. Even greeks themselves had different cultures depending on geographical area (achaens, dorians, aeolians, etc). And Caesar, like again literally every single general in the Roman period, knew very well who Alexander was and emulated him. Greek gods and myths became roman gods and myths, Hercules and Alexander being a huge part of the warrior mythos.
As for Alexander's empire collapsing immediately after his death, it completely ignores the entire Hellenistic period. The diadochi still ruled the vast majority of his empire. Egypt was Ptolemaic, i.e ruled by greek rulers descended from Ptolemy when the romans conquered it. It remained entirely greek culturally throughout roman occupation, like the greek mainland and Anatolia, you know, the nucleus of that little empire known as Byzantine (i.e: East "roman") that outlasted the actual romans by a thousand years.
There's a reason the term
Greco-Roman World is used to describe the culture.
As for aqueducts being a roman invention that barely merits a reply,
http://en.wikipedia.org/wiki/Aqueduct_%28water_supply%29.