From what I can tell, it has to do with the drives mounting on /run/media, and apparently /run is a temp folder or something.
Probably not. Yes /run is a tmpfs, but that doesn’t affect any other filesystems mounted inside of it - those have their own permissions (or don’t in the case of FAT).
Since the drives are being mounted in /run/media they’re probably being mounted by your file manager, not via /etc/fstab. You could instead have them mounted on boot by the root user via /etc/fstab (the classic way) or systemd.mount (slightly friendlier), or configure polkit to allow mounting drives without a password (more reasonable if you’re talking about external or thumb drives).
The permission issue is probably for a different reason. Are you sure the filesystem(s) you’re mounting supports POSIX style permissions? FAT doesn’t, and NTFS requires a special flag for it. The files might look like they have permissions, but they’re coming from the mount options and modifying them will either fail outright or not do anything.
Edit: Run lsblk -f to see all connected drives, partitions and file systems and their file system type.



That would be because every entry (except
/bootand/tmp) is a subvolume of the same btrfs volume. Your other drives just aren’t in there.You might want to read
man fstaband maybe the Arch wiki pages for fstab and NTFS. It’s not that difficult as long as you make sure to not reboot with a broken fstab (usingnofailis also a good idea). And yes you can just mount them to/mediaif you want, as long as the mount point is an empty directory.Ubuntu Studio might have achieved this in a different way but since you’re in Arch land now it’s probably better to do what the Arch documentation recommends.