Basically when u play as a person or 3 man unit you are immortal when you use the trainer, however you can also summon eidolons in this game by sacruficing your partymembers to use them. Eidolons however do not become immortal with the trainer. meaning that if you take too much damage as an Eidolon you will die.
SO's are challenges you can undergo to receive items etc, but when you fail an SO after accepting it you will get auto killed, the trainer does not prevent that.
But in regular combat , you can fight a lvl 99 behemoth as a lvl 10 and you will never die (altho the fight will take a long time ^^)