Backup saves are created at the same time as normal saves. Currently the issue stems from crashes that happen during the saving action. I have made it more stable and it will only get better. This is only the first version after all.
To explain a bit more of the saving system, it currently stages changed and commits them to the save file only every 5 seconds or on important events such as winning a stage, recruiting a character from the banner and leveling up a character.
Savefile cheating is not a concern currently and won't be. The files are encrypted by default but that is not a measure made because of this.
I am sorry for your bad experience, but I hope to do better in next releases. The saving system has been a problem since release and with this being the first official version, it is normal to have bugs.