OK, this appears to me to be not good. I just rebooted as user. I can read and write to folders, but looking at permissions in Dolphin still shows the owner and group both being root. Did some of the above changes give root read/write access to users? My other computer shows the user when checking permissions in Dolphin.
Why do you think that a MS Windows file system (FAT32) understand concepts like user and groups ?
Things are a little different for NTFS, which
under Windows can map it's own users as file owners, but when you mount it on a Linux system things changes and ownership will be attributed to the
user I asked you to put in /etc/fstab.