Yes, I disabled the plugin after importing your field group and the field keys were still wrong. If I delete the field that was created while that plugin was active and then recreate it as a normal text field everything works.
You can’t continue to use that field group. Editing a field will not correct the field keys. The field needs to be completely deleted and recreated.
You may have other issues going on as well, but I saw the same thing you reported, fields not saving. I deactivated the plugin, created new fields and the new fields saved as espected.
