In the movie "Troy," Brad Pitt's character says that the gods "envy us" because we are mortal and that "any moment could be our last." Is there anything like that in ancient writing/philosophy/stories, or is it just another Hollywood good-guy line?

I haven't really encountered anything mirroring this sentiment in ancient literature. The notion of the Greek gods envying mortality is particularly ridiculous if we just confine ourselves to the Homeric poems, in which the Olympians repeatedly pity mortals because they must die. Just another example of how Troy deviates from its source material for no good reason, and of why David Benioff is a bad writer!

As for ancient Greek understandings of the afterlife and such, they were, overall, pretty bleak. The realm of Hades was the final destination for all the dead—there wasn't really a heaven-hell division there, it was just the place everyone went when they died and all agreed that it wasn't as good as the mortal world (when Odysseus visits the underworld in the Odyssey, he encounters many of his dead comrades from the Trojan War, and the impression you get is that they're mostly just bored down there, spending all their time being resentful of those who killed them or who are still alive). While there were some notable negative outliers in the Hades experience like Tantalus, Sisyphus, Ixion, etc., they make up a very small handful of Hades's occupants and only serve to send a message to mortals that they shouldn't mess with the gods.

Elysium does come up in Homer, Hesiod, and some other works of poetry and prose, but its location, features, and entry requirements vary considerably in each. It wasn't until much later in the period that Elysium came to be conceived of as the eternal resting place of heroes and those related to or favored by the gods, and, much like those suffering eternal torment in Hades, only a small group of (fictitious) notables ended up there.

There might have been some belief in reincarnation or resurrection propagated in some of the mystery cults, like the one practiced at Eleusis. We don't have many details about those beliefs that survive, however, so we're mostly in the dark on that one.