I have the basic understanding that the entire plot to Donnie Darko revolves around time traveling. As far as the ending is conceded, you may have various interpretations of what actually happened. The Director's Cut does dive into the book on time travel a bit but leaves me wanting a better explanation for what we see on screen. So what are the common theories to Donnie being dead or alive in both prior to the first plane engine crash and the second one seen in the final scene? Is that enough to understand the overall timeline (which is very complex and super confusing).
I think it is a mistake to take the events of Donnie Darko literally, or to look for a logically consistent timeline or timelines.
There is a key extra scene on the DVD, in which Donnie is having a conversation with his father and says, "Dad, I'm crazy." Not sure why this was omitted, but it strongly supports the interpretation that the film shows Donnie losing his mind -- as do all the included scenes involving Donnie's psychiatrist, who recognizes what is happening to Donnie.
Indeed, Donnie's experiences in the movie are textbook symptoms of schizophrenia:
-he feels increasingly separated from family, friends, and peers
-he thinks he can see into the future
-his fantasies -- like outing Patrick Swayze's criminal character, or (ahem) saving the universe -- put him in white-knight, savior-type roles
-to him, the logic of the whole thing makes perfect sense, but to anyone else, it is beyond comprehension
Personally, I think part of the genius of Donnie Darko is that -- just like many real-life schizophrenics' hallucinations -- Donnie's fantasy almost starts to make sense if you strain to understand. But ultimately it only really makes sense to Donnie.
There is a total of 2 timelines that we observe in Donnie Darko.
The primary timeline, is the one we see at the beginning of the film, starting from Donnie waking up in a random location, biking his way back home. We continue seeing this timeline until the night he first sees Frank.
It is in the next few hours after this encounter, that the Tangent Universe is created. This is due to Donnie not being in his bed when the jet engine hits his room. He is meant to die in this encounter due to some unknown rules of the Universe, better explained in the book. (I think even the book mentions that this can occur for unknown reasons).
During the rest of the film, we are presented the Tangent Universe until the end of the film, when the World is about to end. Donnie summons a portal to lead both himself, and the jet engine back into the Primary Universe, the same night that he left his bed to see Frank for the first time.
It is when we see him start crawling into his bed that we are back in the Primary Universe until the end of the film.
It appears that the film tells the following story:
Originally there was only one Universe - the Primary Universe, where all mankind was living.
At some point in time an "Incident" had happened "when the fabric of the fourth dimension became corrupted and a Tangent Universe was created. There is no indication in the film when this Incident had happened. It may have happened early in the beginning of the film, or at some point prior the events that the film starts with.
As the Book reads, the Tangent Universe is highly unstable and it can sustain life for no longer than several weeks. Apparently, all mankind from the Primary Universe unbeknownst got trapped in the Tangent Universe. After the Tangent Universe expires, it will collapse upon itself, forming a black hole withing the Primary Universe, thus destroying all the mankind.
According to the Book, after a Tangent Universe has occurred, an Artifact may appear. In the film the Artifact was a jet engine that came from the Primary Universe into the Tangent Universe through a portal (gateway) at the Tangent Vortex.
Donnie Darko, now in the Tangent Universe, is chosen to be the Living Receiver with a task "to guide the Artifact into position for its journey back to the Primary Universe". Donnie must accomplish this task before the Tangent Universe expires. If he does not, then all mankind will be destroyed when the Tangent Universe collapses. As the Living Receiver, Donnie is blessed with Fourth Dimensional Powers, most important of which is the ability to create Time Portals (wormholes) - gateways between Universes, that work as a time machine.
Donnie is not aware of his task and his abilities and he discovers them as the film progresses.
People who live around Donnie work as the Manipulated Living, unconsciously assisting Donnie in different ways in his task of returning the Artifact to the Primary Universe.
In addition, Donnie is having visions of Frank that also provide some guidance. In the film Frank is a boyfriend of Donnie's sister Elizabeth, who made himself a rabbit costume for Halloween. What Donnie sees in his visions is not actions of the actual Frank who came back through some sort of time travel, but rather hallucinations that occur because of Donnie's ability of foresight as the Living Receiver. As the Book reads, the Living Receiver is often tormented by terrifying dreams, visions and auditory hallucinations during his time withing the Tangent Universe.
Donnie's girlfriend Gretchen and the actual Frank unconsciously work as the Manipulated Dead. Their task is to create an Ensurance Trap that will leave Donnie no choice but to return the artifact and thus to save all mankind.
After Gretchen is killed in the Tangent Universe, Donnie realizes that there is only one way to save her. By this time he has realized his task and his abilities. Donnie creates a Time Portal (wormhole) between the Universes through which the jet engine returns into the Primary Universe and all mankind is transferred back from the Tangent Universe into the Primary Universe, just before the Tangent Universe has collapsed.
Just before Donnie travels from the Tangent Universe he says: "Going home", and laughs. Then, in his letter to Roberta Sparrow he says: "I hope that when the world comes to an end, I can breathe a sigh of relief, because there will be so much to look forward to". Then we see Donnie laughing in his bed in his home. So, he was glad that he had accomplished his task and saved the mankind. Then he peacefully turns on his side smiling. This suggests that Donnie did not expect the jet engine to crash on him in the Primary Universe, he expected to live on, and thus his act was not a self-sacrifice.
As to all other people, as the Book reads: "when the Manipulated awaken from their Journey into the Tangent Universe, they are often haunted by the experience in their dreams. Most of them will not remember. Those who do remember the Journey are often overcome with profound remorse for the regretful actions ..."
There are a lot of logical problems with this story. Gretchen and Frank are killed in the Tangent Universe, then they are transferred back in time into the Primary Universe along with all other people. How do they become live again in the Primary Universe? Technically Donnie did not return the Artifact into the Primary Universe but instead has sent there a jet engine from another plane. There was no apparent need to kill Frank. Does the Primary Universe become empty when the Tangent Universe is created, is everything transferred from one Universe into another, or only people are transferred and why? Et cetera ...
In my view - a very illogical story and an overrated film.
I tried explaining it here:
Hope this helps