There are two secret movies. Another Side Another Story and Deep Dive, which is an extended version that first appeared in the original final mix. They're both concepts for Kingdom Hearts II. That's it.
I can't say for sure about the requirements, but I know in other KH games you can't get the secret ending by playing the beginner mode so it wouldn't surprise me if the same were true for Final Mix.
Ok I'll have to try it out on proud so I don't have to do ALL of the requirements for normal.