Only thing I could suggest would be opening FPse > open settings > MISC > Backup all files.
It will create a backup of all configuration files, save states.and memory cards on your SD card or your user storage space. They will be in a folder called fpsebackup, inside that is a memcards folder containing slot1.mcd and slot2.mcd. those will contain your savings, I recommend copying them to the directory where.you store your games then just direct Fpse to those files by using the options in MISC settings. Let me know of that helps.
Is the problem you are having that Fpse closes when you load a game so you are unable to open the settings? If so turn when prompted to select an ISO press the back button if you have one, it should take you to a welcome screen which should let you access the settings without crashing.
Edit: I just checked file manager on my phone and /data is empty too, try installing ES File explorer, that is what I use and as long as you have a rooted phone you will be able to access the complete file.system by pressing favourites and going to "/"
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