I think you're confusing the bomb sequence at Sector 1 with the bomb sequence at Sector 5. The first one has a timer. The second one doesn't.
You killed him in one hit because the boss is weak when attacking him from behind. The Big Shot does a lot of damage, and the boss doesn't have much HP. It's early in the game, and they're throwing easy stuff at you.
As for emulation, I haven't had problems. I prefer psxemulator to ePSXe now, but I can run FF7 on both without distortion.