Just how DID Shera survive the rocket launch?

[Skyblade]

She was not in the engine room. She was checking the oxygen tanks. Fuel room, not engine room. The engine room and combustion chamber are probably lower down in the rocket, in an area inaccessible to us in the game. Heat would have taken some time to reach that high, and would only have been a danger during the continual firing associated with liftoff, where the heat would build up in unprotected areas that weren't meant to house the crew during engine firing.

This explains it.

But why is Cid ting his pants about it then? Am I wrong..or does he get all "oh nooooooo get outta there you goddamn waste of woman!" ?

Guess there wasn't a handy EoFF person to cool his guns.

Because had the rocket completed takeoff, the heat would have built up to a high enough level to cook her. It just would have taken longer than the two seconds of firing that happens before he shuts off the engines.

Better question: How did Shinra, in only a few weeks' notice, get an old rocket which had been decaying and leaning over for twenty years to take off successfully and be safe enough for passengers?

Cid and his rocket crew were fanatically devoted to it, and had a lot of time on their hands. They kept the mechanisms in extremely good condition, always hoping for approval. This is explained in game. Their crew has been waiting for launch since that day, all set and ready to go.