Some Questions

[Cruise Control]

First of all, what's up with the saving system? If you go back and replay an old mission, and it saves, will all the save files after that be deleted? Isn't there any way for two people to play the game whenever they want wherever they left off without messing up or overwriting the other person's save files without having two memory cards?

No, it won't overwrite. Theres a mini-savefile created each time it saves, if you go back, it will just update the mini save file for that level.

Secondly, how can I train and level up and get gil without proceeding with the story? The only way I've found is to die in a mission, so whatever you did gets counted as exp, and you can do it again and again, but you have to keep dying to get the exp or gil added. Isn't there a better way?

Not that I've noticed, but I reccomend doing it in the level Deep Ground Strikes back.

Finally, how can I unlock the extra missions? Do I need to shoot memory capsules?

No, those are "hidden targets". You unlock them by beating normal/hard mode. Once you do that go to Extras, and choose Bonus Missionsh, and once you complete one, you unlock the next one. If you destroy a capsule in a bonus mission, you can unlock the next mission without completing the current one.