Despite watching Prometheus and understanding the purpose of the navigation machine, I'm still not sure what was the significance of the space jockey in Alien, specifically...
The Space Jockey is there as a form of world-building, while also establishing some foreshadowing. By including an unknown alien there, it shows that the in-universe situation is larger than the characters or audience is aware, that there is something more that's happened there. The specific point of having its suit show damage that was directed outward shows that something bad happened to it, and it was unexplained. Weapons usually attack from outside inward, but that wound suggests something happened from inside outward.
Why was the engineer fossilized in the chair?
To show the great deal of time that had passed since it had died. Something bad went down here, and no one came to retrieve/save them in that long time since it happened.
Why did the engineer's bio suit show an outward explosion?
It was because the Space Jockey got infected by a facehugger. Then a xenomorph grew inside it, and burst out of its chest. By showing this before the facehuggers were discovered, it foreshadowed the threat they posed to the humans.
This is very similar, thematically, to the start of the classic film The Thing when the Norwegians fly in and try to kill the dog. They both foreshadow a cycle of infiltration and eventually death.
An out-of-universe explanation: the Space Jockey was meant by designer H.R. Giger to be a biomechanoid creature fused to its chair and inseparable from it by design. The Engineers from Prometheus are thus a retcon; the Jockey wasn't originally meant to look so humanoid, or meant to walk away from its seat.
Unfortunately, I don't have a primary source for this, but secondary sources:
Quotes by H.R. Giger:
"The creature we finally ended up building is biomechanical to the extent that he has physically grown into, or maybe even out of, his seat, - he's integrated totally into the function he performs."
"The pilot is conceived as one of my biomechanoids, attached to the seat so as to form a single unit"
Quote by Brian Muir (one of the movie's sculptors):
"I have fond memories of working with Giger. He explained to me and my colleague Peter Voysey that the pilot and cockpit were to be as one, as if merged together.
The inspiration for the final Space Jockey design is one of Giger's earlier drawings from his books Necronomicon, where the biomechanoid nature of the creature is apparent:
Why was the engineer fossilized in the chair?
He was there for a long time.
Why did the engineer's bio suit show an outward explosion?
The space jockey was infected by a Facehugger, so an Alien chest-buster had made his way out of his torso and bio suit.
What happened to this Alien?
He probably died from boredom.
Because despite whatever Scott might claim today, his intention wasn't for the "space jockey" to be one of a race of 9 ft tall anatomically perfect humans.
The implications are quite clear: The "space jockey" was some bizarre life form (engineered or not) to be attached to that station in the ship, never to leave. Even to get up and go to the bathroom. We're not even seeing a suit, but some sort of (endo?) exo-skeleton.
It wasn't a suit in Alien, that was the alien itself. The suit thing was just a retcon in Prometheus which someone has already mentioned.
It means that the ship and the Space Jockey were in LV-426 for maybe hundreds of thousands or millions of years.
The outward explosion shows that a facehugger attacked the being, and maybe the reason it crashed landed on LV-426
The pilot is the origin of the facehuggers. He was not a victim, he was the creator. His vision is distorted by his fusion to the gigantic mechanical phallus. From this fusion, the seeds of the facefuckers emerged.
