Greek civilization would have survived a defeat at Salamis, and the Persians ultimately succeeded in their goal of vassalizing the Greek peninsula through use of Sparta as a proxy, but Salamis established Athenian hegemony and shaped the course of Western civilization.
But that hegemony lasted only until the Peloponesian Wars, which the Athens lost and Sparta won (the fact hardly encouraging for the "Western civilization"

), and ended decades prior to Alexander's birth.
A different Salamis would have meant different Alexandrian and Roman empires, with effects that would be felt worldwide. I wouldn't call it the most important battle, but it was significant for reasons besides the simple fact it was a Persian defeat.
This is, of course, a "classic" point of view but how exactly was it shaping anything in the long term? Persian armies continued their operations in Greece until eventually had been defeated on land and, AFAIK, Salamis had nothing to do with it. Of course, it had its importance but how was it defining anything? After all, Persia was not a major naval power and the fleet defeated was (IIRC) an ad hoc assembly of the ships from the Phoenicia, Asiatic Greek cities, etc.
Agreed with this. While no Hastings would have meant a different English culture, the political and economic trajectory of the island would have been the same whether the medieval nobility spoke Anglisc or French. Without the Norman claim on France, there might have been no Hundred Years War and resulting united France, but it's probably the English would have found some reason to invade anyway.
This was for a while a popular subject on the (now defunct soc-history.medieval) and quite a few people brought up the point that the French (in the "Normandian" version) culture was already penetrating Saxon England. After all, Wilhelm the Bastard was an appointed successor of Edward and Harold had been visiting him in Normandy. In OTL it was a matter of time for the English nobility and royalty to switch to English (well, eventually even the British German monarchs learned the language

). Personally, I don't have any fixed view on the subject except for a purely military one. If we assume that The Bastard id dead (before or during his English adventure), the claim is passed to his sons, etc. and it is a matter of time when the next invasion will happen. And if and when it happens, the chances of Harold or his successors are not good (unless they somehow manage to "normanize" themselves): at Hastings the Saxons still had been fighting in a traditional Norse style: heavy infantry with the battleaxes and short spears, no cavalry, no archers. The Normans already had been ahead heaving all 3 branches and it was a matter of time and tactics to get Saxons out of their good defensive position on the open where they could be destroyed by cavalry. Even if this did not happen at Hastings, the Saxons could not stay on the hill forever, which means that sooner of later they would be attacked while on the march and destroyed (as a side note, Harald Hardrada, who used the same Norse fighting style, was defeated by the Normans in Sicily and there were earlier precedents as well so we have a pattern).
To make the long story short, I'd qualify Hastings as a "token event": it happened and a lot of things changed but something of the kind was almost doomed to happen.
Your point about the 100YW is interesting: of course, if we assume a completely different English royal line, then there is no union of the territories, etc. But most probably this would mean an
earlier united France: Angevin Empire and the later leftover English territories in France had been the major obstacles to the unification process (the last Capetian kings already controlled most of the French territory and Aquitaine was something of a bone in their throat).
As for "unmotivated" English invasion, it is not like Ed #1 was seriously pursuing his claim to the throne of France but he, his sons and his commanders were definitely quite serious about the looting component: England was a relatively poor country but France was one of the richest places in Europe and spoiled by a prolonged peace so it practically asked to be invaded.
