The Film
The crew had gone insane by the end of the film
Its implied throughout the film that staring at the sun for extended periods is playing havoc with some of the crew's mental stability. As such, to gloss over the inconsistencies with part of the films ending/Genre Shift, it would certainly fit with the theme of the melancholic character studies and subtext that Capa (or any of the other crew) had eventually been driven insane by either the futility of their mission or by the sun. This would certainly explain Pinbacker from Icarus 1 still being alive after 7 years with 100% skin damage. Anyone who died as a result was either via their own mistakes, or in fighting (as we saw earlier in the movie, some were already at each other's throats), and any references to a fifth crew member was in their own heads. Whether they still completed their mission or failed is down to the viewer - The Sun being reignited really happened or everything was simply Capa's Dying Dream.- Re: whether they failed/succeeded in their mission: The very last scene of the movie, after Capa dies, shows someone back on Earth noticing the Sun getting brighter again. As that scene is not seen through any of the astronaut protagonists' eyes, but takes place independently on Earth, it indicates that in any case they somehow succeeded in their mission of re-igniting the Sun. However, whether they have gone mad or not during the movie, and whether everything really happened as depicted in the film, is indeed debatable.
Building on that, Pinbacker was a shared hallucination or a hallucination given life à la Paranoia Agent.
He was/is the manifestation of the crew's subconscious fears about their mission failing and everyone being doomed and their insanity leading them to see the sun as a sentient malevolent god-like entity intentionally wanting to destroy the human race. It took the form of Pinbacker because he was the only crew member unaccounted for on the first ship. The air in the big room the explosive material was radioactive or full of harmful pollutants
It's always bothered me that they're short on air but then go into the bomb room and can breathe fine, this is my justification. They knew they could breathe the air there, but due to the toxins in the air it was being held as a last-chance air reserve for when the mission was an absolute "we're not going back". Pinbacker is a cenobite.
He's bald, horrifically disfigured, sadistic, blasphemous, and determined to take the crew to "heaven".- Looked more like a Husk to me. And the madness is fairly in synch with Reaper Indoctrination.
Pinbacker was possessed by a demon.
He really did go crazy, which lead to some sort of sun/fire demon/ghost/entity taking over and turning him into a monster. That's how he drove the rest of his crew mad and killed them, how he survived all that time, and why he stayed in case Earth managed to send another crew up to try and correct the sun. He could have also psychically compelled some of the second crew to want to go investigate the first ship so he could sneak abroad and kill them, which could explain why they did something illogical like that in the first place.- The demon could have even been Satan/Lucifer himself or some aspect of him.
Cassie and Capa were a couple and could have had a child together
Word of God in the background material of the movie states that 1) Capa and Cassie were lovers in an earlier version of the script (and even in the final version of the film where they never explicitly were romantically involved, there is still a strong underlying unresolved romantical tension between them) and 2) Cassie had an abortion after she was recruited for the Icarus II but before the mission left. Now the father is never mentioned in the backstory (only that he never knew of the pregnancy), but putting two and two together... it probably was Capa (also, they probably broke off the relationship prior to the mission, because it was against the rules for crew members to have romantic/sexual relationships with each other).