"Micro Core" is now just "Core".
If installed to hard disk, Core will not copy everything to RAM by default. Instead, extensions (installed applications) are loop mounted. That's what you see with df .
Yes, you can make your customizations persistent.
However, your home directory and the root file system is in RAM by default, so each file you want to preserve needs to be explicitly specified in /opt/.filetool.lst and the backup command needs to be used before rebooting.