We have no idea on any of that. All we learn is that Hawke's character has a pretty good healthcare plan.
From there, we get to Ethan, tending bar in 1970's Brooklyn. All we know is that he's trying to prevent a bomber/arsonist from killing a vast number of people there, and that the date of the bombing keeps changing. In walks another unnamed character, played by Sarah Snook, and the two get to talking because the bar is otherwise empty.
Sarah relates her story to the barkeep, and it's really my favorite part of the entire movie. Hell, it's one of my favorite parts of any movie from 2014.
We learn about the tough life that her role has lived, and how her excellent academic performance and good physical condition led her to apply to a 1950s/1960's astronaut program designed for women... Of course, given the time period, we learn that part of the reason this opportunity has become available is that scientists are worried what those astronauts will do if they can't get laid (f--k you, patriarchal pigs). Rather than being offended or feeling threatened, Snook's part keeps her eyes on the prize.
The story does a lot of things from that point on, and most of them are impressive quite unexpected. As such, I'll leave you to experience the rest for yourself. What I must do, however, is tell you what I liked and didn't like.
I love that this is a science fiction film that focuses on the human element. I've explained this to people before, but a sci-fi film isn't about "people having laser guns," it's supposed to be about how society or the human condition are changed because people have laser guns (or some other fanciful object/invention/etc). To that end, Predestination never shifts its focus off what these SF elements say about humanity, or how they might alter people/society/existence.
Other aspects of the pic were really enjoyable. The method of time travel is absolutely perfect - it has a cool low-tech look, and uses no CGI thing to wow us. Looper did much the same, and I loved the non-fantastical look used there, too. I liked the energy and tension created by Ethan's hunt for a killer. And I remain a huge fan of Gattaca, so I felt a deep happiness at seeing Mr. Hawke involved in another story about some outcast struggling to get into space.
The soundtrack was simple, but easy to like, and used quite effectively. The pacing almost gets clunky at times, but it seems to correct itself sharply and consistently; you stay engaged with the story and the players for the whole running time. The cinematography is quite fine in composition and framing, and uses a variety of nice tricks - again, it's a knowledgeable hand behind the lenses and in the editing room, not a reliance on CGI to dazzle the audience with bright colors.
The real winners, though, are the performances and the sense of ambiguity throughout the narrative. For one thing, we don't know exactly what Hawke's part is up to for the entire length of the picture. Similarly, we are left in the dark as to the nature of Snook's role, the intentions of Hawke's superiors, or the aims of the mad bomber that Hawke wants to stop.
Ethan Hawke is in top form - he plays a nicely-contained protagonist who has emotional motivation yet shows a real dedication to keeping his cool. His familiar face will likely get people to watch this film, and I'm as happy for that as I am for his fine work here.
Sarah Snook, however, is a revelation. I'd never heard of her before, and was instantly taken by the fact that she looks a whole lot like Jodie Foster, but also looks like Emma Stone when she's a redhead. Regardless of her appearance, she's a really good actress - one to watch out for.
Snook neatly conveys the brutal difficulties of growing up as someone different, as an outsider, and inhabits the mannerisms of a precociously-smart individual who uses her wits and sense of humor to deal with life. When she tells her story, you really become engrossed and feel the weight of her character's burden. I wasn't in the mood for an extended life-story, but she won me over right quick, and all these compliments are among the best things you can say about a performance.
For me, though, the problems here keep me from giving it the very high praise that I thought I would give it by the halfway mark. What happens during the last 20-30 minutes does not jibe with what I understand about time travel. While I don't need a perfect scientific explanation or even an explanation for everything that's happened, I suddenly had the feeling that this movie was simultaneously trying to do too much (with its high concept) and too little (with the other elements that help underpin the whole story).
But: other people might not get this sense that the last third is trying too hard to be clever, so there are good odds that you may see Predestination, be blown away by it, and have few (if any) complaints. I've simply read (and talked about) sci-fi too much to not raise my hand and object when the ending of someone's film creates many problems with the story. I'd be less bothered if it didn't seem like those later choices were so unnecessary. It's like finishing a bottle of champagne with one other person and then asking them if they want to go to a bar to do shots...