The liveuser account in the environment you boot from
USB does not have a password, so the usual password prompt gets
just skipped in many places where there would normally be a prompt
for being able to do some privileged operation.
The password prompt that you get while mounting the disk is just for
mounting the disk and not for protecting the contents of the disk. So once you have
mounted it, it tends to stay mounted until you tell Fedora to unmount it
or if you reboot. Until then, accessing the disk would not normally give
you any further password prompts.
Also note that the mount permission is needed regardless of what the filesystem
type is. Changing between fat32 and ext4 will not change this requirement, but otherwise
I'd think that something else than fat32 would be a good idea for a 1 TB volume.
The default configuration in Fedora would allow local users to manage external
disks without extra authentication. However, internal disks are treated a bit more
strictly and there an administrator password is required by default.
If you want to make internal disks mountable by local users without password,
this default policy can be overridden by adding a configuration file with this content
into /etc/polkit-1/rules.d/20-permit-internal-disks.rules.
polkit.addRule(function(action, subject) {
if (action.id == "org.freedesktop.udisks2.filesystem-mount-system" &&
subject.local) {
return polkit.Result.YES;
}
});
If something similar but not exactly this is needed, running man polkit gives
you a description of the configuration format. The action id names for many disk
related actions can be found from the /usr/share/polkit-1/actions/org.freedesktop.UDisks2.policy file.
