Once they die they can't be used in battle again, if you're on classic. I think the ones essential to cutscenes still hang around for them but yeah, you can't select them for battle anymore. My Jakob died in my Chapter 6 Lunatic run and I had to reset because I was fooled by the cutscene too. :(
Is this the ハンデ無しvsハンで有り difference you're talking about? If so the limited mode would be the one that scales the enemies down to your level, while in normal you get a discount on the skills you can buy from the other player after you win. I think.
On a completely unrelated note...
Are amiibo region locked or can I use my Australia-bought amiibo on my Japanese copy of the game?