Well it seemed that Spock was the only person onboard who knew how to jury rig the engines and who could survive in that environment long enough to do so.
No, it seemed like Spock was the only one willing the fix the engines. That's the way the movie presents it. Scotty is literally pretending to be passed out on the floor. Everyone else is standing around with their thumbs up their asses. When Spock goes in everybody is screaming at him to get out. It's like risking one guy to go in to do an obvious job in a room that serves no logical purpose and dying is worse than the whole ship going boom. You know those suits those guys are all wearing? Put a helmet on them and they're radiation proof. That's why Spock puts the the Stay-Puff marshmellow gloves on.
And then, as a final screw you, all the dangerous radiation filling up all of engineering and making Scotty "pass out" disappears except in the room Spock is in.
Khan did say that Ceti Alpha VI's explosion caused a shift in orbit, it could be that each planet realigned in the order of the last to compensate. Maybe a dwarf planet also became entangled in the Orbit and Reliant, carrying outdated star charts couldn't tell the difference?
Discussed this above. No way a star ship's long range scanners would not recognize a change in a system that's this well charted as to have two of its planet's environments well known.
Who says that the Ceti Eel had to be fatal in all cases? Khan said it killed some of his people, some could still be alive.
I have a problem believing McCoy was able to do on the spot brain repair on Chekov considering the thing was crushing his cerebral cortex.