I beat FF6, and after the ending had finished it asked me if I wanted to save my file. I saved it in the same slot as my previous save. But when I go back onto the file, I'm at the same place where I was before I fought kefka. Just wondering, did it save my data? Is Kefka supposed to be permanently dead, or is it normal to save no later than the final boss room?

As for what version of the game I'm referring to, it is the downloaded PSOne port from the PS Store (downloaded onto the PSP in my case).

There is no bonus content which follows the PSOne edition of the game, ergo you cannot continue from the point where Kefka is defeated. If you were playing on the Gameboy Advanced, there is a new lair to explore when the main campaign is finished, and a save is prompted.

The PSX version does have a system file feature though that unlocks bonuses by completing the game - specifically a movie player that allows you to view the CG opening and ending scenes that were added with the PSX version, plus a third bonus CG video put to the orchestrated version of the Aria di Mezzo Caraterre. Plus there's a bestiary of enemies encountered, and an art gallery of cg artwork, concept art and storyboards. Kind of like the bonus features DVDs have.