I don’t think you’re going to get an “empirical” ending, but here’s what I make of it:
Grandma Death has some insights as to how the dead act outside of time to guide and manipulate people on the material plane.
Donnie is sort of a Schroedinger’s Cat. He’s being manipulated by extradimensional entities who have a sort of God’s eye view of things. They are working from outside of time to allow him to make choices that effect the people he cares about.
The entire part of the film in which Donnie is alive is an alternate timeline that exists mainly to show him the options that are available that he’s unaware of. That’s not quite right.
He’s fated to die in a way that seems senseless. The diegesis of the story exists to show him why it’s not actually that bad, and to give him the opportunity to “choose” it. The dead, after their deaths, get “let in on” the joke. Except that part of the joke is that time is an illusion, and so they get let in on the joke before they actually snuff it.
Frank was “in on the joke” at the beginning of movie, which is why he (otherwise inexplicably) honked his horn like a madman when he dropped Donnie’s sister off in the wee hours of the morning. He was trying to get Donnie out of his bed, so that he wouldn’t get hit by the jet engine.
The idea is that death releases you from the point-of-view of the Ego, and makes you aware of the capitalized Greater Good. Frank wanted to save Donnie’s life. (There’s a strange loop here, because Frank wouldn’t be dead if Donnie didn’t survive the accident.)
Donnie’s “free” week shows him that, in some ways, it would be better if he were squashed by a jet engine. He has suddenly fallen in love with Gretchen-- and his sacrifice will allow her to live. It will also allow Frank to live, and, although when he kills Frank, he’s just some jerk who ran over the girl he loved, his enlarged perspective makes him realize that Frank is necessary for his sister’s happiness.
So, in a gross net sense, it’s better for the people he cares about about if poor Donnie lets himself be squashed by the jet engine.
The writer cheats a bit though, and allows the positive changes that Donnie made in the alternate reality to ripple through into the “real” reality. The alternate Donnie takes steps that result in Patrick Swayze’s character being exposed as a child molester, and he also give words of comfort to Cherita (the nerdy girl.) On the night that Donnie dies, Mr. Kiddy-diddling Motivational Speak has a crisis of conscious, without his house being burned down and his kiddy-porn stash being discovered, and Cherita is shown looking at ease for the first time in the entire film. (Speculatively, I think that there may be some connection intended between Gretchen and Cherita Chen, since Cherita is clearly infatuated with Donnie, writing his name in her notebook, and his minor act of kindness with her mirrors his ultimate sacrifice for Gretchen. My take on this is that the writer considers that, with a “God’s eye view,” a casual act of kindness like offering a few words of comfort is pretty much equivalent with laying down a life.)
Donnie laughs hysterically at Frank’s warning because he sees Frank taking an action that Frank must know will result in his own death, and that Frank values a relative stranger’s life over his own. This is funny to Donnie because he knows that Frank is only choosing this because he has the “God’s eye view,” – but Donnie also has the “God’s eye view,” and also knows that his life is worth laying down. Frank is choosing to die so that Donnie doesn’t have to die, but but Donnie is choosing to die (in part) so that Frank won’t have to die. How deep does this recursion go? What was Grandma Death thinking when she stood in the road in anticipation of Frank’s speeding car?
In the context of Donnie Darko, we’re all here to learn that, ultimately, we aren’t worth shit, compared to everyone else. But everyone else has to learn that, too, so that, taking a broad view, it’s a cruel, cruel joke.
The kind at which, when you finally get, you laugh at like a hyena, through the tears, as you wait for that damned jet engine turn you into a fine pink mist settling over your Transformers figures and The Cure LPs.
Yes, I love this movie.