1- The Hellenistic world directly influenced the philosophy of Buddhist and some aspects of modern indian culture

The name of the Greek translation of the Pentateuch is "Septuagint" (in Latin "septuaginta" means "seventy"). The number 72 is justified as 6 elders from each tribe x 12 Hebrew tribes. Some testimonies are quite bizarre, Flavius Josephus gives the 6x12 calculation but he sums it into 70. I suspect some numerological reason behind it, rather than a blunt approximation. Quite probably a motivation for Septuagint was not only the use in Jews religious practice and education but also proselytism. (some of the sources do not say anything about Septuagint being translated for Jews, but for it was worth translating and that the king and his Greek scholars would appreciate such valueable wisdom).

The Celts were far from being "the great bogey-man" of the Hellenistic era, but certainly were a new and dangerous entry in the array of the traditional "barbarian" enemies of the Hellenistic world. Celts entered Anatolia actually as allies being commissioned by the Bythinian king Nikomedes.

Quite...if it wasn't for those ingenius and enlightened Arab dynasties such as the Abbasids and Ayyubids, we wouldn't have many of the classical texts which we have today.

33. During a seige of Athens, the philosopher Epicurus rationed beans to his disciples to prevent them from starving to death. Epicurus taught that the purpose of life was to maximize pleasure and reduce pain, believing in gods that were distant and indifferent to human behavior. Despite this, Epicurus was no craven hedonist. He practiced sexual restraint and lived on a meager diet of bread and water. "Pleasure" for him consisted largely of the warmth of friendship and the joy of intellectual discourse. Despite this, future Epicurians would gain the reputation as voluptuaries.

The bean-sharing is another anecdotical (by hearsay) account from Plutarch. However, Plutarch says that Epicurus shared the beans with his disciples, which means he ate also beans, not only bread and water 

Dexippus, may I remind you the thread in this forum entitled "Hellenistic history - why viewed as obscure" where you together with several forumers contributed in a discussion about a relative lack of interest on Hellenistic rulers, from which Alexander is obviously an exception. This thread was an answer to that one.

However I'd understand much better Aster's point (301 BC marks the practical beginning of the Hellenistic states). The Hellenistic world is bound to these Hellenistic states and Alexander's empire hardly was, especially in its early years. Echoes you'll find everywhere, almost no process in history started overnight. But here we do not discuss such naive visions, but operative taxonomies. I have not encountered any book on Hellenism putting 338 BC as a start. I've encountered few starting their discussion with the reign of Alexander and some more starting with the death of Alexander. Let me give you examples from the latter category:

In Erskine's "Companion to the Hellenistic world":

Part I, Chapter 2 signed by David Braund is entitled "After Alexander: the Emergence of the Hellenistic World, 323-281". Let me quote a bit from it:
"These years show first the consequences of the great imperalist adventure in a a world which, from a Greek perspective at least had now expanded massively. [...] Moreover, it is in these years that monarchy re-emerges as the dominant form in Greek history, after a marked hiatus, with its roots both in Macedonian and local practices. The Hellenstic world which Alexander had instigated was to be a world with great cities - including his own foundations - but it was above all to be a world of kings. Perhaps most exciting and yet most elusive is the rich cultural mix that developed (and not without controversy) in the aftermath of Alexander."

The prestigious Cambridge Ancient History series compiled its volume on Hellenism (VII.1) starting with Alexander's death (however it traces Hellenistic kingdoms only to 217 BC, their last years being included in their volumes on Rome). The second chapter, "The succcession to Alexander" by Edouard Will starts with 323 BC. The chronological table which closes the volume starts again with 323 BC.

That I appreciate, but that still doesn't change the fact that the key defining point of the Hellenistic era is the spread of world Hellenism - for this purpose, the Hellenistic period can only really be said to have begun when this begins to be fulfilled. In that respect, all of our three dates concide except for Choerona, because for decades afterwards, Greek culture was still only confined to the Medditeranian basin and not beyond. Although, Dexippus, your point does lie very much on the crossover point between this idea behind Hellenism. To disagree with it would be pedantic, because it was only a few decades later that the key principle of Hellenism began to be fulfilled. I think that all of our three dates are defensive and have a great deal of points behind them, but I might consider re-evalutating mine because of the many other successor wars that occured before the battle of Ipsus. Also, I've always wanted to write a book...

It is unclear to me that there is a single "key defining point" of the Hellenistic world. I do believe you are correct that the spread of Greek culture and language is a major "theme" of the period--but it is not the only trend.

weren't there steam powered engines in the Hellenistic age?

For Diadochi, I would define:

A - a dynasty that was initially founded by one of Alexander's associates, this includes states like the Attalids of Pergamum, as their founder was himself a decendent of one of these family lines.
B - one which had a large enough Greek/Macedonian population and/or influence in the ruling caste
C - one which developed from the Hellenistic culture above the local culture and stuck to it rigidly (even the Ptolemies adhere to this rule...)

Of the latter

45. Antiochus IV "Epiphenes" was a great aficionado of the gladatorial games, having spent time in Rome as a hostage following the Peace of Apamea. During his reign, he introduced gladatorial style combat into the Seleucid empire. While the bulk of cultural exchanges of the Hellenistic era involved the transfer of Greek culture to the west, the introduction of Roman/Italian style games east shows that the exchange could work in the other direction.